Base 57, that's an interesting idea and although I see the merit of it in certain musical styles I am not sure I would want to go this route in my music. some of it is made for dj's to play and some is inspired by music like kraftwerk. the idea sounds similar to something I used to do as a dj called "riding the pitch" where instead of using my hand on the turntable to gently slow it down I would use the pitch fader and correct it , I usually found this to be the more difficult method as it meant I often lost the nearest pitch point and it was probably the least elegant when listening to my mix. the problem was that there had to be a dramatic shift to counter act the direction the phase was going. usually I could not reverse the phase misalignment of for example a 4x4 kick on two records as that required such a small adjustment on the fader, but instead had to severely shift it in a counter direction then try to get it back to where it was.
when working in the daw with the method there wouldn't be any dramatic changes as it's using much finer adjustment. but, it will still be removing the pitch from the nearest possible place to further away from that nearest possible bpm so this means that correction will have to be monitored very closely to make sure its not corrected too far in the opposite direction.
it could take a lot of time to manually correct the pitch during a song and reverse the direction and study how long it takes to return to it's position I required it to be in and to make sure I don't overshoot.
there are other problems with having a bpm not exact on the grid .the dynamics of plugins that work on a grid and rely on things being in a specific place for them to work best can be dramatically altered. certain types of compression, gating, and lfo along with their adsr envelopes may sound best when locked into the songs bpm as tight as possible and in the worst cases may not be working at all. in one instance I had a kickdrum that completely lost its attack because the plugin moved too much.
there might be a way to get around it using the method you mention, but really I think it would be easier on us musicians to just have the finer bpm adjustment which we can set and forget at the start of the project, we are already part of the way there as cw includes a way to offset the grid so you can start the grid anywhere you like, so if your tracking session has a bit of silence it's a quick and easy way to mark the start of the daw grid. we just need the finer bpm so it can stay on that grid. working with finer bpm in my experience has meant I spend less time on this part so I can concentrate on other parts of the music. recently I had to dedicate a whole day to using the stretch audio method, for me none of the other methods I have tried have been as efficient as working with a fine bpm sub division.