The people in Acorn were thoroughly familiar with 6502 which they used in the BBC computer. ARM was designed by the very same people. They used the BBC micro (and BASIC) for early ARM simulation. They had little money, so ARM was designed to be a very silicon efficient 32-bit processor. They wanted a fast, but similar processor, to be able to (re)write OS and software quickly. On Archimedes, the BBC micro (hence 6502) was emulated (not that it would be impossible to emulate with a completely different architecture, but chips in those times did not tick so quickly so for real speed emulation some degree of similarity was more-less necessary).

The many adressing modes of 6502 is a result of certain nomenclature - it is the same question as "how many instructions are in the instruction set - is mov a,r6 and mov a,r7 the same instruction?". If you rename "zero page" into "register file" and add A, X and Y into the same register file, you will end up with only a few addressing modes, and you will find absolutely the same in ARM's set.

If you are still in doubts, some quotes:
Searching on the web will give more of these.

Today's ARM (and the related approaches) is perhaps slightly different, those are different people and it is a different environment now. They even changed the interpretation of the "ARM" acronym, denying their roots...

JW