"I've been playing Halo 2 online, and I still don't really understand what's so great about the sandbox."
Alright, I can already tell you're new to this, so let's break things down, shall we?
"Players have very few options as to how they play their game. Because there are no armor abilities, players can do nothing more than run around and shoot. No strategy or thinking is required, no way to outwit your opponent."
Saying no strategy is involved is simply not true. In classic Halo, strategy came from micro-positioning, anticipation of enemy movement and tactics, map knowledge, power positions, weapon control, and map control. Halo has always been about those things. If you want to succeed in a match, you and your team would have to control the map and weapons in strategic and logical ways. Get to the power weapons, move to the more defendable and strategic locations, push the enemy spawn... There are a number of ways to use strategy, and there is a lot of thinking required. It just may not be visible right away. Classic Halo games have what is called a skill gap- the difference between someone just starting and an expert is very large and apparent. There are intricacies and tricks that need to be learned and refined over time.
"I used to love sneaking around with active camo in Halo 4 to quietly reach strategic positions and get a jump on unsuspecting players, but the only way to take down an enemy in Halo 2 is to jump in front of his face and challenge him directly, hoping that nobody else will engage you before you finish him off and get back to cover. If one of his buddies shows up, or if he happens to have a better gun than you, you're screwed."
Here's a question: In Halo 4, did you earn that active camo? No, it was something you equipped in a menu. Halo was never about who could abuse combinations of loadouts via a menu. Equal starts meant everyone had the same chance and same abilities as everyone else to do well in the game. It came down to personal skill and strategy. Jumping in someone's face to attack them is neither skillful nor strategic. Hoping someone doesn't show up and interrupt the fight is just plain ignorant. Hope isn't a strategy. You should always be anticipating any possible scenario, and prepare accordingly.
"Otherwise, the battle will simply go to the player with better aim. Both combatants will stand in the open, jumping around like monkeys and emptying their clips until one drops dead. There are no ways to outsmart your opponent, and the only skill a player needs in Team Slayer is that of good aim."
If both players are jumping around in the open shooting at each other and ignoring the rest of the map and the players in it, then both players are performing poorly. Running out in the open is never a good strategy. A player should stick close to cover, stay with his team, move through areas that are confirmed to be safe, be aware and ready for any possibility, and be able to adapt on a moments notice. Outsmarting your opponent isn't done through imbalanced gimmicks like armor abilities. It's done through positioning, map control, and clever movement.
"Escape from battle is extremely difficult due to slow movement speed, as well as overpowered and abundant grenades. Players' frustratingly slow movement speed makes it difficult to avoid grenades (they're everywhere), escape from battle, or traverse cover. Even when bullets are raining down on you and you're trying to escape, your spartan will refuse to move faster than what seems like a leisurely stroll. "
Actually, the base movement speed of Halo 2 is faster than Halo 4. Escape should be anticipated and possible through positioning, not by pressing a button to sprint. Same goes for grenades. If you want to be able to escape quickly and not deal with long range combat, stick to close quarter areas of the map but risk being hit by grenades or shotguns. If you want to be able to have a good view and engage at longer distances, stick to a more open area but risk too many sightlines on you or being outgunned by a better player. This is what's known as risk versus reward. There is always a trade off, and you have to pick your battles and disadvantages to what you feel you can adapt to the best. If there was only one answer to a strategy, or only one way to win a match, then everyone would do that same one thing over and over. This would become boring and pointless. The point of the game is to use the options laid before you to determine how best to go about handling constantly changing battles.
"The game was much better when it had sprint."
This is a very heated topic in the community right now. Much of the highly competitive community would have to disagree with you. Sprint causes many problems. When sprinting, your gun is lowered, meaning that you cannot engage in a fight. Ironically, this slows down the gameplay. You should always have your weapon at the ready. Sprint also affects map design and the sandbox itself negatively. With sprint, a player who made a poor choice can easily escape being killed and punished for that decision. This shouldn't happen, as it lowers the skill gap I mentioned earlier. To counter this, maps with sprint in mind have to be much larger and more bloated, leaving too much empty space for anyone participating in an actual firefight rather than sprinting away. It also increases sightlines throughout the map, making many of the utility weapons in the game (Battle Rifle and Carbine) less useful in what should be their respective ranges of combat. To counter this in the past, these weapons were given longer engagement distances, which caused more problems. Now players were engaging each other at distances where the other two pillars of combat, grenades and melee, were irrelevant. This also caused too much cross mapping in larger more open maps, like in Big Team Battle. So, what can be done to counter that even further? The only logical thing would be to break up sightlines some more. The problem with that, however, is that it would lead to more compartmentalized and difficult to understand maps. Halo maps are supposed to be simple arenas that are easy to learn and understand. People should be able to see each other, but not necessarily be able to engage each other at that distance. Further segmenting the maps would also lead back to the original problem of players being able to escape a poor decision too easily, and the vicious cycle begins all over again.
"The game is very difficult for someone like me who likes to play more carefully. In maps like Lockout, for example, the only way to move between covered positions is to walk a relatively long distance across an exposed walkway or through the central plane area. I hated having to expose myself like this- it's incredibly stressful walking through an open area where it's so easy to get picked off by snipers, battle rifles, or whatever else is out there. The fact that your guy moves like a snail certainly doesn't help."
Again, the base movement speed in Halo 2 is faster than Halo 4. The fact that you're saying the game is difficult after the examples you gave of gameplay lead me to believe you still have a lot to learn about the intricacies of the sandbox, and the strategies that accompany it. Lockout can be a very safe map to move around if done correctly. Again, this comes from proper control of the map and its weapons, as well as an understanding of the map itself, its sight lines, its power positions, its movement options, and the movement of the enemy players. If it's too dangerous to move a certain way, then don't. The nature of Lockout is that the flow is forced through the middle. This is by design, as it's meant to force combat into certain scenarios. These scenarios can be learned and mastered.
"These problems persisted in Halo 3, but Halo 4 solved them by allowing players to move faster when necessary, and giving us more combat options through customizable loadouts and armor abilities."
Just to reiterate: Faster movement isn't the problem here. A lack of knowledge of the game is. I've already stated how sprint harms the game, and loadouts are even worse. They add an unnecessary and unpredictable fourth pillar to the combat that can't be countered in many scenarios. There's no risk versus reward with armor abilities. Only reward. They provide an advantage to players in ways that are different for each person without them being earned or controlled or contested over.
Halo doesn't need sprint to be good. It needs players who understand how to play the game without sprint.
Halo doesn't need extra abilities to be good. It needs players who understand that thinking is the best ability.
Halo doesn't need loadouts to be good. It needs players who understand that weapon balance and control is key.
Halo doesn't need to be dumbed down to be good. It needs players who understand Halo.
