> Shouldn't they be 64 bits on most modern systems then?

Arguably so, but then one would lose the ability to natively name 16-bit integer types because "short" would be 32 bits.

An earlier comment addresses x86-64. AArch64 (pedantically, the A64 instruction set used for AArch64's 64-bit execution mode) is similar, in that addresses are 64 bits wide but ALU instructions typically encode a width bit, called "sf", that selects either 32- or 64-bit data registers and arithmetic. See, for example, https://arm.jonpalmisc.com/latest_aarch64/add_addsub_ext .