Ok, I've figured out what my primary gripe with this game is...
In any game, there are a set of rules which we, the players, are intended to abide by. Think of how, in any Mario game, we need to jump over pits to avoid death. If we fall off the platform, we lose a life. This is the norm and is something I don't think players are bothered by.
The primary issue with Assassin's Creed is that this expectation is not placed upon the player and the game loses a great deal of its difficulty and immersion value.
For example, every piece of advice, be it a hint during a loading screen or NPC interaction that the game gives you, is geared toward having you behave like a true assassin: running instead of fighting, hiding, using stealth, etc. However, the player is not at all punished for not doing any of this. You can run around killing as many guards as you want and as many innocent people as your "health" bar allows since you only lose 3 bits of health when you slay and innocent and these rapidly recharge anyway.
Even the achievements in the game focus mostly on lots of open combat: kill 25 guards in one fight, stay in battle for 10 minutes, let 100 people see you kill someone, etc. It's like the game had this awesome setup where you'd need to play by its rules and then the developers suddenly said, "You know what? F*ck it. Make the player a one man army, god of death where you can hold block and hit X for an instant kill and do so as many times as he/she wants with no fear or penalty."
I thought of what would have fixed this game perfectly: an awareness meter. When you go into a city, it's at zero. As you kill guards, civilians, cause disturbances, etc., the bar would charge up, and if you're running from guards, the bar would slowly fill until you've escaped them and vanished. If the bar fills up completely, your target will go into hiding and not come out, forcing you to leave the city for a while for it to "cool off" from your presence so you'll be able to walk the streets anonymously again, otherwise guards know you immediately and attack you on sight, and maybe an "elite" group of armored, invincible guards show up who you NEED to run from.
With that simple change, it would have forced players to REALLY behave like an assassin, not like now where you can just charge headlong into a group of guards and slaughter them with ease.
The game is still pretty fun, but I wish they had made it more immersive via something like the awareness bar to give it more realism.