Thta's exactly how I have seen it develop, too. A log of the weakness
of the 1H BH is the amount of time it takes to set up; it is not
possible to hit any effective shot from an open position, and it is
hard to really drive a 1H BH unless you are there in plenty of time,
get turned, get set, and take it a little in front. Other than that,
the best you can hope for is a neutral shot (basically, re-shuffling
the deck to see what your next hand will be), or worse, some form of
slice to buy some time.
The 2H BH completely and forever changed the game. It was always
easier to go after anyone's 1H BH than it was to rally forever to
their FH--besides, I'd get tired and/or make a mistake. It wasn't just
me, either; most competetn club-level players did exactly what you
described: wait for a chance to bully someone on the BH side, either a
FH to BH exchange, running aorund one's own BH to keep the pressure on
their BH, or else try the approach you suggested.
As much as I liked hitting 1H BH, when my daughter came to learning
how to play, I thought long and hard and could not think of any
compelling reasons to use anything other than a 2H BH. You really only
give up the ability to slice to get to the net, which few do well
today, or to change pace (rhythm) with a slice.