The magnetic leakage of the R-core depends on the windings. With primary and seconday of separate sides for good isolation, the stray field is no longer that good. For a good stray field if would more need 2 x a split bobin.
Yeah, there are some misrepresentations in this thread... If you wind P and S both on each bobbin, you get flux cancellation per bobbin, low leakage (comparable to, or maybe a bit better than, a shell-style transformer), and modest capacitance (less than toroid, but maybe same or more than shell).
If you wind P and S on separate legs (whole bobbin P, whole bobbin S), you get maximum leakage, which leaks out into the space between windings. Capacitance is minimum, though still not terrifically low because the winding-core capacitances will be modest, and you get half that because they act in series. (Maybe with a special bobbin that gives more airspace between winding and core, you could make a medical-style low capacitance unit?) Grounding the core acts as an electrostatic shield (and an additional shield could be placed between windings in the middle, to get ~total shielding), reducing transfer capacitance but increasing individual winding capacitances (since they act to ground, rather than in series with each other). A heavy copper flux band around both windings would be highly desirable to short out leakage, improving regulation and reducing external fields. Mere copper foil will not do the job: this will carry some amperes at full load.
Compare the leakage path between bank-style windings on an EI core: P/S are side-by-side on a single bobbin, so the leakage is the space between them (and some of the space around, mainly in the volume where the windings stick out from the core). A flux band helps here, and modest thickness copper is adequate to short out the relatively small volume. This style has usually 10 or 20% regulation (worse in smaller sizes, I think?), so the separate windings R-core style (or sectorally divided toroid, equivalent to it) will have even worse regulation (30, 40%??) without a flux band.
I've seen a few R-cores myself; they may be more common in Europe, not sure. As far as shape, it's a low-profile design, but unlike a toroid, the rectangular form may give other options in a tight layout.
Also once saw a low-profile shell-style transformer, EI lams, but very stubby 'E's so it was quite short, and a long stack of them to make up the difference. The winding window was nearly square. Kind of like an ELP ferrite core and bobbin you'd see these days, but in laminated iron instead. Probably more expensive due to the wasteful* cut, not to mention the low production quantity (just judging by how infrequently I've seen the style, I mean).
*Default laminations are "wasteless". Consider the 'E's butted together tip-to-tip, and the negative space between them (what will be the winding area) equals the 'I' piece.
https://www.seventransistorlabs.com/Images/Wasteless.png A bit larger winding window is usually desirable (accounts for the extra insulation needed in a build), hence ferrite shapes usually have a relatively wide winding area for example; but it's not such a big deal for steel, and is cheap enough I guess, compared to having to scrap the difference.
Tim