Some common architectures like x86 can suffer from an issue called partial register stalls. So from a performance perspective choosing a 32 bit integer can be better.
You're confusing things. It's one thing to claim that either they never used a feature or they even have a personal preference to do things one way or another.
Another entirely different thing is to proclaim a programming language designed to target any conceivable CPU architecture somehow no longer needs to support basic cpu arch traits such as word size.
As I pointed out,there are still processors being sold today that do not support 32-bit ints. If you expect C to be able to target these architectures, obviously this feature is still a critical feature.
Also, people who maintain yesterday's systems that require non-32bit ints still need to work on them.
Chesterton's fence is still relevant. Why are we pretending that it's ok to mindlessly proclaim a feature is not requires because we don't understand why it was necessary to begin with?
word sized variable is relevant for performance, it is processed in exactly one cycle (I strongly suspect there is an asterix somewhere).
Most notable uses, where int makes sense over int32_t: array indexes, for-loop variables, enum, flags.