I think Julian is pretty much spot on.
“remote focusing” (effectively treating the smartphone camera like an eye, and thus requiring an ocular in our optical train) is possible, but only over a fairly narrow range limited by aberrations and the range of the smartphone sensor.
Some lower-mag systems (like IOLight and Grundium) use something very similar to a smartphone lens as their objective, which means it’s small enough to actuate with a voice coil or piezo. However, for oil immersion it’s pretty hard to take that approach, hence our slower-moving objective.
The autofocus procedure takes a few seconds per position, which it would be nice to shave off. However, at the moment the slowest part is acquiring the images because of (1) settling time and (2) transferring a high quality image out of the GPU and onto a disk. So it might help, but it wouldn’t be a 10x improvement. It would, however, require a pretty massive software, firmware, and electronics redesign, that we don’t currently have the skills or resources for. If you do, and you fancy implementing a smartphone-style imaging unit (one that doesn’t depend on disassembling consumer electronic devices for which there’s no spec sheet), it would be very useful to lots of people!