TL,DR; I don't think being slow makes you crash into people, there may be correlation but it's not causation, so I don't agree that lower DR's should have multiple races in the FIA part of Sport Mode.
Long version:
I don't really get the connection between slower drivers and dirty drivers. Just because you're DR-D/C/whatever doesn't mean you can't run behind someone without punting them off.
If you regularly punt people off, brake earlier and lighter than the car in-front, increasing brake pressure as they slow further so you don't clean them out.
If someone overtakes you on the inside while you were doing this (happens to me a lot) let them go and know you probably should of been covering the inside. If you can run through the next bend side-by-side do it, but know it's risky and they may not give room (may not be a clean driver).
Try and get your nose at least 50% past before attempting to out-brake someone unless you trust them. (if they cut you up, and you're over half way past on the inside, you'll win)
Use radar
Give space to someone going for the inside (what exactly would cutting them up achieve if they've committed? They may just fly by having outbraked themselves, for you to just cut back, cutting them up would of ended your race.)
If you really don't want them to try it, cover the inside, but then you run the risk of being passed on corner exit (these decisions are part of the fun of racing

) or punted off (annoying)
And the main thing to remember with Sport Mode is not winning is fine. I haven't won a daily in weeks, 50% through DR:A.
I know there will be people that just don't take it very seriously, and wiping out half the field is just a laugh (not in a dirty troll way, but, it may be they just have a very casual approach to it), "oops haha". But I know to some people it's more serious, and when you're really trying and someone "oops, haha"'s into you it can be extremely annoying. Best thing you can do is just keep on trucking, keep trying and the good races will come, especially as the game ages, the more casual people will either get better or stop I think.