What's wrong with that? It might be just a bit slower but for me that kind test is a lot of comprehensive. I have in the past has to slightly change the DB schema. Because of full stack test coverage were in place, full functional tests make all the bugs caused by schema change visible immediately.
For me, schema changes in DB cause some other operations to the DB failure is much difficult to detected and fixed if the issue is not visible to the developer immediately.
It might be slower (~a few minutes for ~300 full funtional test scripts run directly from the web-browser side) instead of seconds in your case, but I think the time is well spend for how quickly complex issues can be discovered and fixed.
BTW, I keep track of all DB operations (sql query) time as part of the json response. If they are > 1 milliseconds (SSD HD), I will flags them as potential issue in bugs DB for future investigation for SQL optimization.
It should be easy to add the SQL query response time to a performance DB to track and change over time/sw version.