Same reason that x86 became hot, really. There are these newfangled PCs/smartphones that are providing ridiculous volumes that create network effects and defray design expenses. Back in the day the idea of x86 in a server was crazy, but they were able to break into the server market from the bottom and mostly consumed it. The same might happen with ARM, or it might not since Intel is in a better position than the RISC vendors were with it's near monopoly giving it access to phenomenal engineering resources.
> Intel is in a better position than the RISC vendors were
Actually, Intel might be in a worse position with respect to vendor lock-in. I'm guessing a lot of early servers' lower layers like OS, webserver, etc. were proprietary; convincing the vendor to support x86 would have been a hard sell; and porting your application to an x86 environment was difficult.
All of these things would have had a tendency to lock people into their existing hosting choices.
Nowadays most servers run mostly / completely FOSS (at the lower layers) that can be easily ported to ARM. I'd imagine porting code to x86 from VAX or DEC or mainframe or whatever, was a lot more painful than porting PHP, Django or Ruby web apps to ARM today.
Of course, Intel does have deeper pockets and much of the desktop market, and may well be able to use that to keep ARM in check despite the fact that switching CPU architectures is probably much easier for website owners today than it was when Intel was trying to break into the server market.