Because an enterprising engineer managed to hand code an assembly language implementation of cellular baseband on ARM thus entrenching ARM as the low cost implementation on a cell phone. After that, ARM expanded outward to run the GUI.
In addition, the batteries of the time demanded a specific power envelope. Not many chips had this envelope ... pretty much only ARM , MIPS, and a handful of also rans that you've never heard of.
Once ARM got going, network effects took over. There is no reason you couldn't implement a cell phone on a MIPS core, for example, at this point except for network effects.
Another thing is that at the time only other ISA designer that really cared about this market was Hitachi with it's SuperH (and then founded Renesas with the sole intent of becoming meaningful ARM competitor, which obviously didn't happen).
You could get usable low power microcontrollers and almost-SoCs with ARM cores in late 90's. While there were SoCs with other 32b RISC cores they typically were intended for mains powered high performance applications ranging from DVD players to network equipment. See how large part of Freescale's PowerPC SoC lineup are without much exaggerattion "Cisco 2500 on a chip" (obviosly with ppc core instead of m68k and with wonderfully complex DMA-engine/protocol decoder/whatever-thing)
Wasn't ARM also the de-facto standard for PDAs? Which was a deliberate market profiling after Apple came into the fray and wanted a CPU for their Newton (and helped spin off the ARM we know today from Acorn).
Low power Intel is not as good as low power ARM. "High power" ARM competitive with desktop doesn't quite exist yet, although the iPhones are very close (and better than a desktop of a few years ago)
I would imagine it comes down to margins. In a competitive market, customers aggressively try to drive down prices. Most silicon companies are too smart to play that game. You fight to establish dominance up front. If you don't win the market, you're unlikely to every become profitable, so you cut your losses and exit.
In addition, the batteries of the time demanded a specific power envelope. Not many chips had this envelope ... pretty much only ARM , MIPS, and a handful of also rans that you've never heard of.
Once ARM got going, network effects took over. There is no reason you couldn't implement a cell phone on a MIPS core, for example, at this point except for network effects.