Can you elaborate on what “standard and effective workarounds” you are referring to here?

Connection pooling is the most obvious one which is so common it tends to be transparent and built into many DB access libraries. Then there are all sorts of proxies/load balancers/multiplexors. If you think about it, the bits of code that handle web requests in your typical web app/framework/whatnot are very much like lambdas and when you write those, you generally don't have to worry about the cost of DB connections because it's a well-solved problem.