Remote database -> massive response time increase?

Yes

90-100ms round trip + time to prepare SQL statement + time to execute statement + time to send results back multiplied by the number of times you need to query the database.

Sure the connection may stay open but it’s an inherently expensive thing to do.

Considering that some setups can respond in full in less than 100ms never mind the database connection, you should look into co-locating your database and your server, if not on to the same machine but somewhere very very close.

WordPress specific things that may help include:

  • Object caches
  • Database query caching
  • fewer SQL queries
  • Use of transients to store the results of expensive operations

You can see what SQL queries are made and slow queries using tools such as the query monitor plugin