The most common constraint is whether the DB as a service offerings support a given extension, since they don't support installing custom ones. Naturally choosing to support an extension across a fleet of hundreds of thousands of instances (running dozens of different minor versions) isn't a decision made lightly, so it can take a while for new extensions to be supported.

Supported extensions on AWS RDS: https://docs.aws.amazon.com/AmazonRDS/latest/PostgreSQLRelea...

Supported extensions on Google Cloud SQL: https://cloud.google.com/sql/docs/postgres/extensions

Supported extensions on Azure Database: https://docs.microsoft.com/en-us/azure/postgresql/single-ser...