Thanks everyone for replying. I was confident in my stance that everyone belongs in a team fight no matter what, but this is a mentality that I'm finding hard to discover in other assassins that just want to roam and leave the big work to everyone else.
I play Jax and Poppy as assassin characters, and I always try to be present for a team fight simply because its necessary for everyone to be together and to provide the big burst of damage the team needs. I'm not perfect with my timing, targeting, or positioning, and honestly I don't believe anyone else is. But I try my best, and that's all I demand of anyone else and hope that's all they demand of me. The negativity in this game is the biggest killjoy, and I often just put my chatbox to the bottom of the screen and pretend there is no smacktalk going on. It helps me focus on the GAME too, so I usually don't need the chatbox for communication since I can see what's up without distraction. The game in question was one such game: after 20 minutes of their **** I just put the chat away and focused on the game.
I know that's bad of me, but I would rather enjoy the game with no ****-talking and lose as opposed to getting upset over comments and losing. Very few people know how to be constructive or helpful for being so "pro". IMHO it shows their true professionalism by being little children over a game, and honestly a pro should be in ranked, not normal matches.
Actually, I disagree..
Not all players should be in all fights at all times no matter what. It depends a lot on how much map control you have and the positioning of both teams. If you have 2 mid towers (of the enemy) down, it's often best for 3-4 of your teammates to press tight up against the last tower to wear it down and attempt to pick enemy players off..
In a situation like this, it's almost useless for an Akali, or Nocturn, or Eve, or even Vayne to sit with the team. If they do, they just run the risk of getting picked off themselves. It's much better for one of them to run to a side lane, get some gold, XP, maybe jungle a bit and get buffed, and then when a team fight DOES break out, the rush in and take out anyone with 1/2 HP or less.
This helps them get more gold and XP than the average enemy (as you are essentially neglecting them of XP/Gold by pressing them back against their tower and harassing them). It also allows them to "patrol" the jungles and the buffs to make sure no one is trying to sneak off and come back to your team with an advantage.. And it ALSO helps your outside lanes push so that you control more of the map.
IF, however, your team is the one being pressed up against their tower, then yes, assassins should generally stay very near by so they can assist in taking someone down when it comes time to.
But if you have map control, there's no reason an Assassin or a Pusher (Mordekaiser, Sivir, etc) shouldn't be off in an outside lane farming and pushing.
If the map control is 50/50, and it's very back and forth, then the Assassins should be how was described above: Jungling and farming a little bit but generally playing relatively close to the team, although not directly in the middle of it.