Moving to Intel chips did two or three things for Apple:
1. It helped them jump from a failing CPU platform to a non-failing CPU platform. PPC was not keeping up with x86 anymore and Apple's two PPC vendors were going in opposite directions because there wasn't enough of a market for CPU's for Macs. (There were even rumors of future Power Macs migrating to a full POWER CPU rather than PPC.)
2. It meant you could run Windows, and hence Windows apps, on your Mac if you wanted to, without CPU emulation. This is still a fairly important use case.
3. It may have also simplified matters even for Mac application development, since you didn't have to switch ISA's in addition to switching operating systems. Making matters worse, PowerPC defaults to big-endian and x86 is little-endian.
How does this apply to a potential ARM switch?
1. You can't really say x86 is "failing" if it's still the industry standard, but Apple might believe (rightly so, given the market size of iOS) that they finally have the ability to sustainably outperform the performance of x86 on their A-series chips.
Most of the PowerPC bet was that a newer and more elegant architecture would outperform x86 and provide Apple a competitive advantage, and while that may have occasionally been true sometimes, it was never a huge deciding factor. Intel and ARM kept up because they were able to make investments in keeping x86 afloat. Ironically, Intel themselves also bet that a newer, more elegant architecture would make x86 obsolete, namely Itanium, only for AMD to invent x86-64. Not even Intel themselves could stop the x86 train.
With the rise of mobile devices, ARM now has the same market power as x86, if not more, simply because there are many more ARM-based devices manufactured and sold than PC's. Apple in particular has been able to invest heavily in their A-series chips and has full control of their CPU roadmap and destiny. Perhaps this time, x86 may finally be rendered obsolete. Don't count on it, though.
2. This is really mostly dependent on Apple's strategic priorities. With more and more application functionality moving to mobile and the web, being able to run Windows is less and less important. At the same time, being able to run Linux is more important; for many developers, running a Linux VM in Vagrant or Docker lets us develop in a similar environment to the servers our code will eventually run on. Sure, you can run Linux itself on ARM, and perhaps there will be more Linux distros that support ARM when and if Apple switches the Mac, but it won't actually be the same as the server unless ARM makes serious inroads in the server market.
Maybe they're betting they can surpass x86 enough that they could emulate x86 at respectable speeds. Since they would be migrating CPUs again, they will probably provide a CPU emulation layer again, like they did when migrating from 68k to PowerPC and then from PowerPC to x86. Keeping this emulation layer around would have more of a benefit because, after awhile, nobody needed to run 68k or PowerPC code anymore. This has never been true for x86 code, and it won't be for a long time, so look for Macs to continue to run x86 even if Apple switches.
3. I think A-series is also little-endian by default, and for x86, see above. Maybe Apple is banking on getting more value by running cross-platform iOS/Mac apps than cross-platform Windows/Mac apps. This will probably impact Mac gaming the most, but that's never been a priority for Apple.