Why Cannot Intel Compete Against ARM by Sticking with x86?

If Intel and AMD sticks with the x86 architecture, why would they have problems competing with ARM-based CPU manufacturers?

The problem with this question is that it is the wrong question. The question that should be asked instead is:

Why cannot ARM-based chips compete against Intel and AMD?

In the past, especially Intel has had a massive advantage controlling large foundries producing their chips, and their chips only. Because these semi-conductor foundries where at the leading edge making the smallest transistors, Intel could beat all the competition. Why did Intel have such a lead in manufacturing silicon chips? Because of volume. Intel made more chips than anybody else, and with volume follows economies of scale.

A Semi conductor Foundry, where silicon chips are made. Intel used to have the superior ones but have since lost their lead to TSMC.

Yet they no longer have that advantage. The Taiwan Semiconductor Manufacturing Company (TSMC) has beaten Intel at their own game. And there was always just a question of time before that happens.