Yeah, none of the rest of the big three are asking you to pay anything for those masters at this point, though. "They're your nodes, you paid for them" seems like a reasonable position to take here.
If that were a reasonable position, you'd think AWS RDS and Google Cloud SQL would give you superuser access to your database instances to do things like installing Postgres extensions.
It seems a lot of people are happy to pay for instances they can't even SSH into. :/
Unless the point of your server is to provide SSH (you are using it as a development box, maybe?), having to SSH means that you are lacking in the tooling department.
At work we are guilty of that. We are actively trying to improve on this.
(Disclaimer: I work for GCP, sorry for not making that clear in the parent comment)