Nobody is disputing the definition of beta, I just merely mentioned that beta and correlation are two separate concepts. In any case, the definition of beta is (mainly) for portfolio to broad market, even estimating beta for a single stock to broad market is a fishy proposition. Many stock pairs have stable, invertible short-term hedge ratios measured in a number of different ways. People actively and successfully trade stock pairs in delta-1 space on much shorter time horizons, so no reason to expect that it would "fail" in the options space.
the problem comes when you start saying your gonna "finance stock A calls by selling calls in stock B" recipe for disaster lol
What exactly is the problem with that statement and with the trade specifically? The fact that you have never done conditional spreads does not mean it's a "recipe for disaster".