Have owned and loaded for too many rifles chambered for other small centerfires, including the .25-20 and .32-20, to be "hostile" to small centerfires that aren't .22's. I'm just wondering why spend what will probably be considerable money just to be able to handload cheaply--and the rifle probably will have to be pretty expensive in order to shoot super-accurately. Then there's the expense of a wildcat, which I know all too well.
But if I was bound and determined to create such a cartridge, I'd probably cut off the .22 Hornet case enough for minimal case capacity with .25-caliber bullets. None of my several references on wildcat rounds list such a creature, but it's probably been done already.
It would then be possible to get a Hornet rifle rebored to .25, whether for airgun pellets or .257 cast bullets. Both cases and rifles are pretty common, and reboring would be reasonably inexpensive.