Check out this fascinating article: "The Best Bunters of All Time:"
https://www.beyondtheboxscore.com/2012/12/10/3748738/best-bunter-all-time-career-bunt-hits-bases-empty-mlb,
According to the research in this piece, a significant number of well-known hitters have had extraordinary success bunting for a base hit. The numbers I'm going to cite are all based on bases-empty bunts, since otherwise it's hard to sort out bunts for hits from sacrifices. The full story is in the linked article.
Mickey Mantle is tenth all time in total bunts for base hits at 80, with a .541 BA (reaching base, 54.7 %). Brett Butler is #1 in total bunts for hits with 188. Butler's BA as a bunter for hits was .488. For perspective, #5 on the total hits list for a bunter with the bases empty is Kenny Lofton, at 123 hits with a .537 BA.
Career-wise, Lee Mazzilli is tops for bunting BA at .875. Steve Garvey is #3 at .821 BA, Nellie Fox #4 at .814 BA. #10 for bunting BA was Pete Rose, at .699 (65 hits in 93 attempts).
So, maybe
the real problem with SOM's "bunting for a hit" model is that it doesn't offer a high enough success rate for these premium bunters. If success rates like those were possible, I think that bunting for a hit (especially to lead of an inning), might have become an extremely popular strategy. I might be OK with having the Mick bat .541 in a leadoff role some of the time, and definitely .875 for Mazzilli.
I've never been a big fan of the bunt, so I found the above data eye-opening and surprising. Maybe today's hitters might try bunting against the shift sometimes if they could achieve results like this. (Note: the article also gives a "reached base" percent that's usually a little higher than BA, presumably because it includes errors, but I decided to cite BA since we all know what that means.)