Doesn't x32 only have four registers available in the calling convention, AX-DX?

The stdcall calling convention used APIs and API callbacks on Windows x86 doesn't use registers at all, all parameters are passed on the stack. MSVC does support thiscall/fastcall/vectorcall conventions that pass some values in registers, but the system APIs and COM interfaces all use stdcall.

Windows x64 and ARM64 do use register passing, with 4 registers for x64 (rcx/rdx/r8/r9) and 8 registers for ARM64 (x0-x7). Passing an additional parameter on the stack would be cheap compared to the workarounds that everyone has to do now.

The x32 ABI uses the same fastcall convention as the regular x86-64 ABI. It's mostly syscall numbers that are affected by the shrunk pointers.