If I buy a theoretical stock for $10 and it splits, now I have 2 $5 stocks.
Total cost = $10
Total value of stock = $10
If that $5 stock goes up $1, and I have 2
Total cost = $10
Total value of that stock = $12
If the stock never split, and it goes up $1 I have
Total value of stock = $11
Every dollar earned on the split = double the $$ earned on your principal.
You got your math backwards.
However, what I think you are trying to say is, IF the stock moves up $1 post split, it would only move up $.50 pre-split.
That would assume that the market was logical. It is not.
How do you think Microsoft got its billions of market cap (still double that of Google, despite it's lowly $27/per share)? When each share got really expensive, it split, and MORE people bought than before.
Let me ask you how comfortable you are buying shares of Berkshire Hathaway A (BRK .A) at $107,998 each? The 'usual' 100 lots is $10,799,800. Well, I don't have any. I wouldn't put that many eggs in 1 basket. And it moves up a big $120 at a time. Stable, but sort of pathetic (unless you count yields). It stays stable because few can afford it, and those few generally don't pay attention to the market and let it ride. Berkshire rarely has to panic sell to cover investor withdrawals.
Contrast this with penny stocks... look at the price actions, they can quadruple in a day on ANY news... you can be wiped out in hours playing them.
The higher priced your stock, the fewer people want to buy it because most people want to buy in round 100 lots. It makes for lower volatility on that stock as well as presumably you have less speculation. Good for Berkshire, bad for fast money.
The cheaper the price, the more 'affordable'. This is human psychology. Of course there are exceptions, like Google, but that's because goog is the flavor of the moment.
Therefore, when the stock is cheaper, the price tends to move more. Add to that the REASONS a stock splits (good news, anticipating faster growth, don't want their stock to be priced out of reach for many investors), and you have a nice combo.
This isn't always true as I said before. Crappy stocks try to split to bank on the split mythos too... so without strong research, you can still lose your butt... and as you pointed out... 2x faster

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I am not teaching anything, this was just random commentary. What works for me, may not work for you, so don't pay attention to my rambling please.