Yes, rust hasn't been eliminated entirely, ,but (largely) gone are the days of MOT failures from rust. I had to replace both the sills on my 1980 car in 1989/90. My other cars of that era were similarly bad at that age.
Most cars got scrapped at that point in time.
Modern cars typically are still in excellent condition well beyond that age, without needing any welding, but cosmetic rust issues do arise from time to time.
The comment about design life being shorter now - I can see a conflict for manufacturers, because short longevity will correlate with (or cause) poor reliability. If a car becomes a lemon, it might harm the manufacturers reputation.
Toyota traditionally top reliability scores and presumably value that reputation and work hard to maintain it.