It is often NOT the controller causing that, it is lag / network jitter. Most controller users are fairly smooth.
Nearly all those that aren't smooth are not using the analog sticks to steer, they're using the d-pad. Regardless of whether it's a controller or wheel, if the data flow from their console to yours isn't smooth or is missing a significant number of packets, the result you see is jerky driving. Making "wheel only" lobbies would not solve this issue and would unfairly exclude a large percentage of controller users who are skilled enough to be predictable on the track. Note that this uneven data flow can be caused at any point on the path between you and your opponent. It could be their connection, it might be yours, or it might be some piece of internet hardware or data traffic congestion on the route in between.
If you're seeing a significant percentage of drivers exhibiting this jerky driving, it may be of some benefit to investigate the stability of your own internet connection. There's any number of free tests available on the internet, here's one I picked at random from a google search that includes a jitter measurement:
https://freeola.com/line-test/ The jitter number should be as low as possible for good results and if you and your opponents both have stable, low jitter connections the tolerance for high ping is actually a little better.
Edit: As a reference, my ping to that site is in the 250ms range but jitter was only 1ms. This is a very good result with a ping that high. The longer the travel time, the more scope there is for variations in travel time (jitter) between packets.
Also, I use a wheel and regularly race with a number of controller users that are not an issue on the track. One in particular is close to the fastest driver I've ever had the privilege of sharing the track with.