Why wouldn't they do this on their own? Keeping their reputation good with all countries(even the oppressive one's) is an important part of business. After all, amazon has stakeholders to answer to.
I don't see how it hurts their reputation to allow Signal to anonymize. They could even block domain fronting in general to block bad actors, and quietly whitelist Signal.
It's not about anonymizing, it's about hiding under the mask of some other entity, without their(other entity's) permission. AWS's other customers and various governments won't be happy about aws allowing Signal to do so.
While they could white list Signal, I don't see why they would want to go through this trouble. It's not like any of these public companies care any more about supporting people under oppressive rules, than profit.