On the other hand, an ARM-powered desktop would be limited to iOS apps and won't be able to run OSX applications, like video games and word processors and whatever else...
I think its a fairly safe bet that they're not going to pull an ARM-based iMac out of their hat today. However, as part of a longer-term project there's no reason why a big, wealthy firm like Apple couldn't address all of the problems you list, especially since they're the unchallenged experts when it comes to switching platforms between processors (68K to PPC, PPC to Intel).
Much recent, well-written software could be easily re-compiled for ARM by flipping a switch in Xcode (old, legacy-ridden code like Adobe CS might take longer). For everything else there's translators like Rosetta.
To replace Intel in their higher-end desktops, they'd have to come up with desktop-class ARM processors, possibly with PCIe support and OpenCL-compatible graphics. ARM is a hugely flexible platform designed for third parties to play 'pick'n'mix' with the individual modules of a CPU, plus Apple have a history of working with ARM (pretty sure they owned part of it at one stage) so while that isn't going to happen tomorrow, its not impossible.
...meanwhile, ARM processors have more than enough grunt for web browsing, word processors and email, especially when coupled with dedicated chips for video decompression etc. (e.g. the $50 Raspberry Pi, which is pretty feeble even by ARM standards, quite happily plays back full HD video).
The better question is "why?" - and the answer to that would be that ARM allows Apple to effectively design custom chipsets to fit their products, rather than build products around whatever chips Intel deigned to produce.
I don't think its very likely, let alone imminent - but its a lot more feasible than some people let out.