I'm a huge fan of Lambda and use it extensively at work, but IMO at the point where you need to solve the problems this solves, you should transition out of Lambda and onto something like EC2
Out of curiosity, if this were to solve problems with endpoint pricing and cold-starts, then what other problems do you see that would still force you to move over to EC2? Just wondering, I've used Lambda a bit but never at scale and these are the only two problems that I can foresee.
The other problems aren't technical, stuff like how much you could save by moving off lambda and lock-in (There are enough subtle differences between serverless providers to make migrating not exactly turn-key)
I see Lambda as a springboard for rarely used or short lived applications. I wouldn't build a core product on it