Presumably because, if the average small business with no net profits went up to a VC and asked for $3m on a valuation of $100m, it would be laughed out of the room.

I'm inclined to agree with you, but AFAIK the word "startup" was invented by small companies which desperately wanted to convince investors that they were absolutely determined to become large companies. So I'm not surprised that it still carries that connotation... the real surprise is that the connotation is wearing off. We're getting to the point where your proposed definitions sound more and more reasonable. Because it no longer takes five years of advance planning, an enormous staff, office buildings, multiple factories, and all the other big-company trappings to scale up a small company, if that company is on the web.