A better solution may be to make a progressively harder problem

I thought this was the whole point of the rising difficulty.

No, the rising difficulty of bitcoin is that each has goes from 1 in 100 to 1 in 1,000. So, you just have to do more of them. In this scheme, the little guy with a single computer gets left out , left in the dust.

What I proposed was a rise in difficulty of further hashes. So, 1 in easy, 2 is hard, 3 is very hard...

So, each person running a node, could easily do one hash. And thus it would become standard that everyone runs a node that can, because anyone can get lucky. Right now, if you are not doing terrahashes, you aren't even playing. (or, in other words, cars and bicycles need not apply, when racing rockets and supersonic jets)