Overwatch has a post-match reputation system where you can vote for players who were good team-mates, good organisers, etc. I don't know how the practicalities of a system like this could work in GT Sport. You couldn't necessarily connect the votes a person receives to their SR - too much potential for abuse. If you set up a system where a certain number of negative votes sent a message to that player then anything could happen - they feel persecuted and stop playing, they decide to play the spoiler deliberately, anything.
If it's done anonymously, unlike Overwatch, then there's a chance of it working. Sport Mode has races of 12, 16 or 20 cars, so say you can vote on 1/4 of the drivers - 3, 4 or 5 per race. There's a chance the post-race chat could have people saying "everyone report ____ plz dirty" but it would vary how much people followed through on that.
A system like this is a good idea in theory, but it would probably only work if every player is explicitly trying to race fairly and as well as they can, and every player is committed to playing the game regularly. Ironically it would be, like the racing and penalty system already is, dependent on all errors and mistakes being honest, and every player constantly committed to improvement. I don't think enough of the playerbase would use the outcome of votes like this in the manner they were intended.