I don't think there's ever been much of a perception that there was a gap there. It's been there for 110 years, and the only attempt to split the difference hasn't done particularly well. This is primarily because the .450/.400 worked so well and was so successful - more double rifles have been built in .400 than any other over .40 caliber. It wasn't on the slow side. It set the over .40 flanged nitro velocity standard that the others followed. If something larger were desired, a .450 was the next logical step.

No, the .500/.416 doesn't require a larger frame. It hasn't set the world on fire because, as good as it is, it suffers badly from the perception that it kicks as hard as a .450 or .470 and crowds the pressure of the .375 Flanged Magnum (the price of breaking the velocity pattern). For that reason it's usually skipped over in favor of either the .450/.400 or .470. Nice .400s are as easy to sell as .470s these days.

Same issues as the .500/.416. A rifle for a straight case .423 with a 450 grain bullet at standard velocity will weigh just as much as a .450/.470 and produce just as much recoil, so why bother?

...and that will drive the pressure up well over .375 Flanged Magnum levels with a straight case. Seems like everybody is a velocity hound these days. None of the over .40 flanged nitros ever did that in the field, and all were successful and proved more than adequate.