The ranks for different roles idea won't work

Right now, League’s ranked system rewards specialist players

It doesn't.

Right now, if you don't play all roles, you are on the same playing field as everyone else minus a few autofill games.

This is basically equal. You can carry to the same elo as anyone else in a single role or multiple roles. No reason to give people special treatment because they are capable of playing all roles to the same level. The whole point of League is picking what is optimal for you, making this forced system where everyone has to play everything is one step closer to having random roles in ranked. In fact at that point it basically is. It's just blind pick.

One solution here could be to have an overall rating (or link all existing ratings) to keep the match competitive.

Creating a system that arbitrarily hurts players who don't play all roles is not a "solution".

You already have the solution right now - the current system.

This new system biases it in favour of players who play every role to the same level.

The whole point of League ranked is you play your best, this system would force you to play your worst like a normal game.

There is no reason to implement this, I see nobody asking for it as well

If we do move forward with this (nothing locked in yet!), we’re gonna have to solve these problems in stages,

This is the LAST thing League needs.

A lot of players like me don't play support because they find the whole role boring, unsatisfying to play and just not good, so I avoid support.

If I'm forced to play support, you have forced me to stop playing League because I won't enjoy that at all, especially if you tie my entire rank to all the other ranks including support, meaning if I don't rank my support in games I don't enjoy I will be well below my actual skill level in my best roles.

TL;DR: We believe having ranks for different positions could be a big improvement. However, there are a number of tricky problems we would need to solve before introducing something like this.

There isn't any way you can make this system work with me playing the game. The current one is fine, please stop changing it to "fix" it.

Forcing me to play a role I hate and don't enjoy just to get a real rank is not an improvement on the current system. In no way is it in improvement. It is anti fun and would ruin the game. There are no solutions to this nor are any of the suggested solutions even vaguely close to achieving the actual solution; which is having a single rank like now.

Single rank gives you a single goal to work to, I don't want 5 ranks and a chance that I get queue up in the wrong one because of what the system chooses for me. That is just horrible.

If I queue up to play League with one game to play and one rank, I level my rank. I don't want to have a random selection of ranks I may or may not get the opportunity to rank up depending on whether the game lets me or not.

That's just ridiculous. Not thought out at all and can't ever work.