This is not going to be an easy question to answer...
Each role has sub roles. Fighters have duelists (good to great sustained damage), assassin-like fighters (lots of burst, but unlike duelists there's short cooldown time between bits of damage), and bruisers (high base damages, lowish to medium scaling), for instance.
Supports have tanky CC machines, utility bots, and even mages that simply let the ADC farm because they already killed everyone else. Tanks have some champions with high damage, and some with low damage but insane CC. It goes on and on, depending on how many times you feel like dividing up each role. You can honestly divide them down to individual champions, and if you really want to get picky you can divide each champion by build.
The real question you should be asking is how much damage should my team have relative to other things, like utility and bulk. Poke compositions want a lot of damage for sieging, but they also need utility to assist against engagement teams, or bulk to protect from counter poke. Protect-the-carry comps want more utility and bulk than damage to literally do what the name suggests.
Split pushing comps, however, want a slightly less utility and bulk than protect-the-carry comps, but they also want their damage to be spread out. They will be focusing on smaller engagements, with many of them being while outnumbered.
The real key here is being able to adjust builds in champion select depending on what your team needs and what the enemy team has. Jarvan is a good example. He can provide the utility and bulk some compositions desperately need, however if your team messes up and you need to take on a more engagement heavy, assassin style for smaller fights you still can. You have to be able to look into what your team's cards are and how they will play out over the course of the game in both winning and losing situations.
TLDR: There's no set answer to how much damage each role should do. It's just one of the highly volatile elements that helps keep League fresh to many players. Just keep an eye on what your team has picked in champion select and do your best to judge what kind of ratio your team's fighting style will need between damage, tankyness, and utility. If you do that then at least the role you're playing will have the proper amount of each for what your team needs.
