That's all plausible except the price issue. Say, you keep 10 containers alive, so you make 10x 100ms calls every 5 minutes. That's gonna be $0.20 per month. 20 cents.
For example if your sign up process is lambda you did you got your cost benefit analysis wrong on anything other than a prototype or mvp, but if your 'change your profile photo', something that maybe happens a handful of times across a month on average per user at best, and you implemented that as your lambda to reduce load and delay scaling needs on your core infrastructure then that feels like you did it right.