Your experience doesn't surprise me. Flat-tipped mono-metal pistol bullets create a large temporary wound cavity (rather than fragmenting) by driving a large pressure wave in front of the bullet on impact. I'm sure that's a very effective way to kill a rabbit--evidently (per your report) better than any fragmentation produced by drilling the same mono-metal pistol bullet and hoping for fragmentation. (See e.g.
https://en.wikipedia.org/wiki/Terminal_ballistics#Flat_point or
https://www.ballisticstudies.com/Knowledgebase/The+Effects+Of+The+Meplat+On+Terminal+Ballistics.html.) Perhaps there's not much fragmentation because the bullet isn't going fast enough to fragment when it hits a soft target.
A pointed, jacketed, cup-and-core high-powered rifle bullet hits the streets going about three times as fast as a pistol bullet, and carries its velocity a lot better than a flat-tipped pistol bullet. Putting a hole in the tip lets the jacket peel away from the core on impact. A bigger hole creates more edge to catch and pull the jacket away from the core, and I believe more pressure inside the tip pushing the jacket outwards. The higher speeds of rifle bullets mean the forces pulling and pushing on the forward edge of the jacket are greater than they would be on a pistol bullet. So drilling the rifle bullet's tip affects its terminal ballistics very differently.
I do a lot of varminting with a 22-250 AI and a 243 Win. (Responding to those who suggest I practice shooting rather than tinkering with bullets: this past summer I made 95% of my shots on prairie dogs out to 350 yards in 5-20 mph crosswinds. I doubt most of you can shoot any better, and I really doubt most of you shoot hundreds of rounds a year at varmints alone.) My Nosler and Hornady varminting bullets have plastic tips plugging fairly large-for-caliber holes that result in great external and terminal ballistics both, the latter because the hollow-tipped bullet expands explosively on impact. My Sierra varminting bullets don't have the plastic tip--just the large-for-caliber hole in the tip. Either way: the faster the bullet and the larger the hole in the tip, the more explosive the impact (that is, the more rapidly the bullet expands on impact). Varminters who want to preserve their coyote pelts use full-metal jacket bullets (pointed tips with no hole at all) precisely because the lack of a hole results in the bullets not expanding on impact. They poke tiny holes that a good taxidermist can easily repair and hide. (Some coyote hunters tell me they hunt with 223s for the lower muzzle velocity. They don't want the explosive impact of a light, frangible bullet going really fast.)
The same thing happens on big-game animals. Other things being equal, a bigger hole in the tip of a cup and core bullet results in the jacket peeling away from the core more rapidly on impact. So if you have a cup-and-core bullet that opens too slowly on impact for your taste, you can alter the terminal ballistics by trimming the meplat or drilling the tip (or both). Of course, you can also just buy a different bullet, as many on this forum have rightly suggested. But if you've bought several hundred cup-and-core bullets for hunting, and you discover they don't perform the way you want, or if you just really like the external ballistics of a particular target bullet and wish they had good terminal ballistics, all hope may not be lost.