Certainly our AWS bill when we were using Lambda + API Gateway forced us to "think about servers" and why we were paying 10x more for slower responding application server to spin up for 15 minutes to process a request that requires 50mb of RAM / 10 ms and subsequently billing us for the full allocated amount at 100 ms. Learn from our pain: use EC2.
How much traffic were you receiving when it made financial sense to switch from serverless to EC2?
I mean we only tolerated those bills for a few months before we had to switch, but generally speaking we were handling on the order of 4-5M requests/day, mostly low bandwidth. API Gateway, and wasting lots of allocated server resources for each time the function ran, was just killing us. The load was pretty constant, which was another reason to switch. No regrets either way, but we should have done the billing math at production load and not just been blinded by the free tier and the low cost per run.