Anywho, the cases are not precisely the same. There is a difference in valuing what you already possess against what you can potentially gain, against what you can potentially gain vs. what you can definitely gain.
You just cite economic tenets, which do not really apply here. No interest is paid on the
actual possession of Bitcoins, so early crediting does not improve profits. Maybe you understand it, when you look at an opposite projection: falling USD/BTC and difficulty. By your logic solo mining would become more profitable, because your probability to find a block would be shifted into the future into lower difficulty territory (just as the higher difficulty territory in your projection). Both projections are false. Solo and pooled mining have identical returns on average with a slight advantage due to fees and less stale shares for solo mining.
Furthermore going back to the original point, all statistical probability requires a large sample, in the case of mining bitcoins, this sampling is time. If I flip a coin one time I have a 50/50 chance of either result. If I flip it twice, same thing. By your logic no matter how many times I flip it, betting on heads will yield the same results, which is completely untrue. Given a large enough pool of flipping it will come out 50/50. But on a small scale betting heads every time can yield profit, or loss. Large numbers and small numbers are not equivalent.
This really shows the barricade in your mind pretty nicely. On a small scale the average return is 50/50, just as in the large scale. The chances for loss and profit balance each other out exactly. Variance is variance, limiting it may have value to some, but it hasn't anything to do with average return.