When amd64 was released, x86 was almost ubiquitous on desktops and ran the majority of servers - most of the software used by the world could continue being used. If AMD had not gone through this effort to make it backward compatible, it's likely IA64 would've won and we wouldn't have this debate. Hard to understate the importance of not breaking things.
If you were designing a greenfield 64-bit ISA, then yes, it might make sense to have `int` be 64-bits, but it was definitely not, and still is not a mistake that it's 32-bits on amd64.
On RISC-V for example, it's questionable. The RV32 ecosystem is tiny and almost irrelevant - if they decided to break things for RV64 it wouldn't be a big problem - probably better to fix any problems early rather than hold baggage to run software that never existed - though it's much easier to port software to RV64 if `int` is still 32-bits.