I fully agree with you. Based on my experience, Lambda is perfect if you only want to perform some relatively standalone task (such as a compute intensive rendering). As soon as it needs to connect to 3rd party entities, it becomes very slow and loses some of its benefits. Connecting Lambda to an AWS DB for example is challenging to say the least. It also takes a couple tens milliseconds just to setup the DB socket and connection, that on a normal server can simply remain open and wait for the next request.

Serverless is nice, but the ecosystem of serverless tool is really missing today IMO