ARM SoCs support OpenCL, too, so they can make use of the GPU for filters and image processing. And typically, the GPU is many times faster than the CPU when it comes to such operations.
Writing speed of storage is also not an issue. You gotta realize that cameras can take RAW images at up to 40MP on a class-6 card (maximum 6MB/s write speed). 20MB/s is luxurious.
Seriously, we had Lightroom and Aperture back when Pentium 4 was around. And we were running Photoshop on Pentium 2 and 3. Your typical ARM smartphone/tablet is now at least comparable to Pentium 4 level, but with much faster solid-state storage. There is no excuse. In fact, I'm a developer myself, and I have played extensively with image processing in one of my recent projects, so I know exactly what these devices are capable of.
I could write my own photo management app, but then I don't have the time to single-handedly write in RAW support for the thousands of cameras out there. That's the biggest showstopper for me. But sincerely, as a developer, I don't think Lightroom or Aperture on iPad or iPhone is impossible.
I would think you'd want to process images much faster than you can write to NAND at 20MB/sec, otherwise trying to process 16GB of photos on a phone is going to take a while.
And back in 2001-2002 when a Pentium when a Pentium 3 was all the rage, normal people weren't dealing with 16MP images.