Bitcoin Mining profitability depends on ... of course, in this case, how many people join the pool.

Not sure what you mean by that.

In this model three cases are considered where the difficulty grows quickly, very quickly, and very very quickly in the DownCase, Case, and UpCase respectively.

Looks to me the other way around - in the DownCase the difficulty grows very very quickly.

Furthermore:

In all cases it seems the revenues drop too quickly. Increases in difficulty are due to hardware advances and BTC rate appreciation. The part related to the exchange rate doesn't affect the dollar revenues. Hardware advances are mainly due to Moore's law, which is about x1.5 per year. There can be some rapid growth until the ASIC transition completes, but after that x10 per year is way too much.

Mining has fixed expenses depending on only the hardware and method used. It seems you modeled the profit as exponentially decreasing, where in fact the revenues are exponentially decreasing and from those constant expenses should be subtracted.