No one said ARM would instantly replace X86 hardware, there would be no reason for it.
But software will follow hardware, if Intel _would_ suddenly, or even over a period of time, increase prices to an extreme amount both companies and consumers would opt for the much cheaper alternatives that would crop up. Especially companies, once the price points of hardware outweighed the cost of porting to a new architecture... it's porting time. And once companies start switching it will trickle down to consumers faster and faster, much like how windows is used the most common in business and so is also most used commonly in the home since it is what the PC purchasers were familiar with.
Basically you have the time T1, the span of time where prices start to increase to the breaking point and the time T2, the span of time from the price breaking point, where life of the hardware in use should last. T1 + T2 would be years, possibly up to a decade or longer depending on hardware stockpiles.
That is more than enough time for things to be ported. Even if it was a short lead up time, I am very sure Microsoft and Apple, much less Linux, would have very little trouble coming up with something like Rosetta, the program that let Power architecture Mac software run on Intel Macs on their own OS.