Lambda is too expensive at the moment, sure. But I think we all know that the costs will, over time, go through the floor, and in 5 years time nobody will want to create server software using anything else.
Predicting the future is a job for fortune tellers, not developers. Being sure about what will be the cost in 5 years is beyond fortune telling. Based on what I know, my company will continue to have on-premise servers and all the companies in the sector will continue to do the same. "server software" is not just Internet software, the world is larger than that.
I disagree. Whether it's a good design depends critically on what the future holds. Will costs go through the floor? We should, and can predict this.
What does it cost to host lambdas? Not a lot. So we are good from that PoV.
Will it be commoditized, or will there be crazy markups? Can any random guy set this up? If you really want to check this, try setting one up yourself and see if there are any roadblocks. (I didn't)