You don't need a large driver and in general it's a lot less random than a few weeks ago, however there are a few troubles with it (but those might've been present from the start and just covered up by the random driver mistakes). On some tracks a short one qualifies better, but on average over all tracks a large has an advantage. For an individual, especially 15 race, calendar that's not a given, though.
Just passing on what I was told direct from a support agent. Qualifying is well and truly broken in my opinion. Every race we see the same tall drivers at the front and small ones to the rear. Why don't the devs admit there is a major issue and deal with it instead of unnecessary updates. Fix the other issues first.
It is true that there is a problem with the height of the riders, in fact tall riders are favored, but with the same height, however, the qualifications favor who has the best car for that track (except for "some" "bugs" or for those who abuse the bug to change their strategy just before the race).