I think the idea is to use their "enterprise", paid offerings as opposed to relying on the "free" services that Google or Microsoft offer.

No.

The main issue raised several comments up is portability. No provider locks you to only using their email offering/cloud offerings if you register their domain through them. Even if they did, transferring domains is trivial and well-supported everywhere.

As far as any other objections people usually raise around using hosted email and the like, a domain really has no comparable privacy implications in the real world (you're not handing Google or Microsoft a huge corpus on your life). It's also through their enterprise offerings where as long as your bill is paid they're generally not going to have some automated review suspend your account with no reason, and if they did they have actual support you can get in touch with.

This solves basically all of the problems with using an @gmail.com/@outlook.com/etc email address.

Google, Microsoft and AWS offer registrar services becuase it keeps you in their ecosystem for their higher margin products. THey generally offer competitive pricing for things like doamin registration and don't pull stunts like charging 2x as much for "privacy protection" or the even more dirty tricks like godaddy and other bottom feeders.

I recently trialed hosted email with AWS and while it is very basic it only costs 4/user/month - cheaper than my google apps service. I was also able to register a new domain at market rates and get dns automatically setup (I think?) on AWS as part of the service. Now because I tie my monthly AWS spend with my registrar I'm more confident I can get some customer service as well.

staying inside a vendor's ecosystem for very selective services can actually work out quite well, as long as the seller/customer incentives align and they are relatively commodity services.