> You are assuming that the amount of work is finite, so more productive people implies fewer people are required. Is that the case though? Has it ever been?

How many horse farriers have you met? How many coopers, blacksmiths, or shoemakers?

The amount of work is not a fixed number, it's more of a supply/demand curve. Do we need 100 programs? Yes definitely! 10k? Yes. 1m? Probably. 100m? Uhm... 1bn? Probably not.

So there will always be a point where people aren't willing to hire more software developers because there are enough already.