The advantages of a baseline grid are primarily related to both efficiency, speed and keeping various elements, like body copy, cutlines, bottoms of photos, etc., lined up. Once that grid is reduced to 3- and 4-pt increments, I no longer see the point of having one since positioning starts approaching being arbitrary anyway.
Just using your example of 10/12 body copy, I might decide that in a particular magazine the author’s byline looks best when set in 13pt type with the writer’s title set in 9/10 pt type immediately below it. I might decide, in that same publication, that credit lines for photos need to be set in 6pt caps with 4pts of space between the cap height and the bottom of the photo. Cutlines in that same publication might look best at 11/14. I might also decide that I wanted the leading between bulleted items to have an extra 5 points of leading.
I could go on, but my point is that, even though all these things might look just right to me, the inconsistencies in the measurements just don’t lend themselves to lining up to a baseline grid. Yes, I could start making compromises by shifting things by two or three points here and there to accommodate a modified baseline grid that’s been divided up into smaller units, but this brings me back to what I just mentioned about the advantages of a baseline grid becoming less and less meaningful once that grid is chopped up into smaller units.
Baseline grids also get in the way of dealing with orphans, widows, articles that are a couple of lines too short or the insertion of odd-ball elements of various sorts which I could write an additional paragraph or two about. My point, though, is that for some things, like books, scientific journals and other things that depend more on structured consistency and efficiency than they do visual dynamics, a baseline grid can indeed be one’s best friend. For the other things that require a bit more fluidity, they can be a counterproductive pain in the butt.