The only reason why rimmed cartridges should be considered more suitable for Handis is they're generally low pressure and they worked best in ejector barrels which have a bad habit of causing failures to eject(FTE), but even that can be avoided by not using hot loads and working with a clean, polished chamber and tuned ejector ala FAQs.
But H&R no longer makes ejector centerfire rifle barrels, hasn't for several years, so rimmed or rimless even in a high pressure round is a moot point. Even ejector barrels can be converted to factory extractors at home or by a gunsmith, so that makes the FTE problem a non-issue, the rim isn't a saving grace, it's the pressure they operate at and the breech thrust created, I've had FTEs in my 405Win H&R with max loads, it's a rimmed round also. On the other hand, I had no FTE's with the experimental 300WSM at mid level loads under 60kpsi, it has a rebated rim, those loads were just too much for the frame due to the huge case head and caused internal action flex, but they never did FTE in the ejector barrel.
The only failure to fire issues I've had that I couldn't attribute to bad primers has been on the 45-70 Ultra which has a too deep rim cut, too much headspace can affect rimmed rounds just as easily as a rimless round.
Tim