Actually, it seems to me that with the .22 WMR and .17 HMR we have the high velocity rimfire market pretty well bracketed, no need to split the difference. If there is a market for any new rimfires it would be on the larger side. I've just been reading Townsend Whelen's book "The American Rifle" published in 1918. He praises the .25 Stevens rimfire as a great small game gun with more shock than the .22 LR while not blowing up small game like a higher velocity round will do. Perhaps in new production they could offer two loads, the original velocity of @ 1150 fps with a lead bullet and a high velocity JHP load at @ 2000 fps. The only problem Whelen saw with the .25 rimfire was that the smokeless loads ate up the bore in just 500 rounds due to the corrosive priming. That would not be a problem today.
I also think there would be a market among those who don't reload, for some larger caliber rimfire pistol rounds. I bet cowboy action shooters would like to see a return of the old .44 Henry rimfire if the ammo cost could be held below the centerfire rounds.
Of Course, there is also the problem of convincing firearm manufacturers to produce guns for the new round.