What if the dividend is 8% and the stock price has the potential to more than double?

You'd miss out! On that one.

But the "shotgun" approach is a game of statistics.

As you note, sometimes a yield is high simply because the stock is oversold, so the price rebounds. It's not that rare.
But on average across all US stocks with yields that high, that's not the case. Somewhat more often it's because the dividend is going to get cut and the forward total return will be poor.

If every quarter you built an equally weighted portfolio of all the stocks covered by Value Line with an indicated yield over 8%, you would not do well.
Total return including dividends since summer 2007 of -9.5% (total, not annualized)
Versus S&P +334.6%
(and, just for completeness, a portfolio of all those dividend payers paying less than 8%, +312%)

So the conclusion, and the reason for my suggestion:
In the very specific situation that you know nothing else about a company besides its dividend yield, you want to skip those over (say) 8%.
Maybe you prefer a cutoff of maximum 7% of 11% or whatever, but there is definitely a level beyond which you'd better have some other good reason to want to own it.

Jim