As you yourself said. Your load is so light you keep it in free tier. Their entire business model is for them to capture you while your load is light and then when you scale the price goes up.
But the price per unit of measurement goes down, so no, it's not "their entire business model".
I have also used lambda at scale in professional environments. I would not use a lambda for a webserver at scale, but having an s3 object trigger processing via a lambda function is a really nice flow.