With a couple of exceptions in the enthusiast sector, where they are well regarded. Or at least they did at one point. I am of course thinking of the cars with the 1JZ and 2JZ engines. I have an inkling that my heuristic might also correlate with Yamaha input, but on that I'm not certain (not knowing the whole engine lineup)
Nope; both are like that now. They used to make fun cars for people who love driving. Honda held out some five to ten years longer than Toyota, that's all.
Actually, I agree with you. The Supra seems to be an exception to the rule with regard to Toyota culture. It's fascinating and I'd like to test drive one.