Possible; IIRC, we had the same thing on x86 because the jump to AMD64 meant that you could depend on certain extensions (SSE2?) that didn't exist on all previous processors but which were present on all 64-bit processors. So it became a split where code compiled for 64-bit CPUs knew it could depend on those extensions without even needing a runtime check, which was nice. That said, my understanding is that for data-heavy workloads it really does help to move twice as much data per operation.
'int' size stays the same. 'long' gets bigger (on LP64 platforms).
Apart from that, I would agree with your assessment.
I'm sorry when I was in university there were still SPARC64 machines around, which use the "ILP64" where the default int size increased to 64 bits, so that must have been why I was taught that the default int size increased when going to 64-bit arch.
In fact, hypothetically assuming the same instruction set, 64-bit can cause performance degradation over 32-bit, particularly in memory-bound benchmarks, because the size of memory pointers and default int size will take up twice as much space, which puts stress on the limited cache space, which will generate additional off chip memory accesses.