Currently, the only plane that seems to not suffer from wonky ground handling is the Milviz C310R. I can’t speak from experience because (as you already know), I’m not a pilot and base my view solely on seeing tons of real aviation videos on YouTube. I never see any of them struggling to maintain the centre line as badly as I am in MSFS. I don’t know what they did, but whatever it is, it works well. I can generally maintain the taxiway centre line without much effort, whereas with pretty much any other plane, I’m pretty sure I look like a drunk navigating the plane down the taxiway.
The Carenado Mooney used to have excellent ground handling as well. It used to be by far the best. But when they launched their update that made it Xbox compatible, it seems their ground handling went down the ■■■■■■■ and it became just as squirrely on the ground as any of the other planes.