Why is the amount of RAM usable by a computer limited by the processor bits? It isn't. Historically it hasn't been with examples where address size was bigger or smaller than the "bitness" of the CPU.
Look at 8 bit CPUs like the 6502 & Z80 that addressed 64KiB. The 16 bit 8086 addressed 20 bits and the 16 bit 80286 24 bits.
On the flip side, the 32 bit Motorola 68000 had 32 bit addressing, but only ran 24 bits to wires limiting it to 16MiB. Which is the approach of the x64 chips I know of, they aren't running 64 lines to the outside world.
When the 32 bit architectures were being laid down, 4GiB of memory was pretty much beyond comprehension. The 80386 was introduced in 1985. In 1996 Microsoft releases MS-DOS 3.2, which still limits the maximum size of a hard drive partition to 32MiB. Very few people were thinking of GiB hard drives, let alone memory. SPARC was introduced 1987. PowerPC 601 in 1992, now we are getting close to GiB hard drives if not there yet. Unix workstations might have two digits worth of MiB RAM. The need for more than 4GiB was still a long ways off. Adding the hardware and complexity of supporting greater than 32 bit addresses was not worth it.
Once an architecture is laid down, and in use you can't easily change fundamentals, like the size of address. One can add on, like PAE on the x86, or external memory controllers on a 6502.
Edited to add
And the reverse happened also. The IBM 360, introduced 1964, was a 32 bit machine with 24 bit addressing. The CRAY-2, introduced 1985, was a 64 bit machine with 32 bit addressing. (If I am reading this brochure correctly, See "Architecture and design" starting page 6.) Note, the CRAY-2 appears to be 64-bit word addressable, so 32 bit addressing would give an address space of 8 * 4 Gi or 32 GiB.
I've been talking about address space. The question title is about RAM. RAM, absent an external memory controller that remaps memory, is going to be limited by the number of address line wires coming from the CPU. Some CPUs had fewer address lines than bits in their address space. A famous example is the Motorola 68000 that had a 32 bit address space with only 24 address lines. Another example is Intel's 80386SX, again 32 bits of addressing and 24 address lines.