Think about it this way though. If it was profitable to pay amazon to do it even with them taking their cut, it would be much more profitable for them to do it

Think about it this way though. If it was profitable to pay amazon to do it even with them taking their cut, it would be much more profitable for them to do it themselves. If it was more profitable than renting out the performance to other people, it would be the lowest hanging fruit by default. This isn't hypothetical, the CPU mined coins aren't close to profitable with web services. And the people making profitable ASICs are using them rather than selling them because it's intrinsically more profitable.