What the is frequency with which a bridge partnership is dealt hands suitable for bidding 2-over-1?
i don't have access to hard stats, but based on my 4+ decades of playing competitive Bridge that figure rings true. If we consider a 26 Board Duplicate session as a typical evening, our side can be expected to open the bidding 13 times, with perhaps 6-7 of those being a Weak 1NT opening or 1 of a minor, perhaps 3 being opened above the 1-Level either weak or strong, and  the remaining 3-4 being opened 1 of a Major. For two of those to then employ  either the Forcing 1NT or 2-over-1 response, the two key system bids, sounds about right.

Remember that 2-over-1 is designed as a teams-of-four system that trades off weaker performance in part scores for increased accuracy in slam bidding. This leverages the IMP scale to best advantage, but can hurt MatchPoint performance. For a pair with specific aspirations in MatchPoint events only the switch you describe might be worthwhile - it certainly worked for Barry Crane, who shone in both team and pairs play with a system designed very much for MatchPoint (and Board-a-Match) events.