I'm not a big Win 94 fan, and think the Model 92 is better suited to the .44 Magnum anyway (being designed and sized for handgun-sized cartridges), but there are certainly worse things.
I always like to say I don't think much of pistol caliber rifles either, since if carrying a rifle around, it might as well shoot a rifle cartridge.
But then I look at what I own, and see I don't practice what I preach. I've had at least one pistol caliber rifle since 1985, and have them in a few different calibers now. I don't have a lever action .44 Mag right now, but do have a Ruger 77/44 (.44 Magnum). It goes to the range almost every time I go. In fact, although bought for no good reason, that 77/44 has become a candidate for my "lightweight general purpose rifle".
I'm a fan of Jeff Cooper's Scout rifle concept, which, as originally defined, was a lightweight, handy, general purpose hunting rifle. It was capable of taking most game the average hunter would ever see, and handy enough to always have handy.
I have started to think the .44 Mag rifle might serve the purpose in dense cover areas. The .308 would also, but my 77/44 is at least two pounds lighter than my Steyr Scout .308 (which is super light itself). Where I live, the terrain can be dense woods in one area, then wide open fields a quarter mile away, so I couldn't say it would cover everything around here. If you stayed in the woods though, a .44 Mag rifle sure would do the job.
A few years ago, Indiana opened up the deer hunting regs to allow pistol caliber rifles- the first time smokeless powder rifles have been allowed in decades. I've been entertained watching some people think they need to shoe horn the largest cartridge possible per the rules into a rifle. I guess I need to spend more time in the woods, because I have not seen any elephant-sized deer.
My back trouble has ended deer hunting for me, but all reports I've heard show the .44 Magnum rifle to be just wonderful on deer.
I have loaded everything from 240 and 300 grain Hornady XTPs, cast bullets ranging from 130 grains to 320 grains, round balls, multiple round balls (two .433 balls), and shot loads in my Ruger 77/44. Almost everything shot at least as well as expected (the shot loads were pretty dismal) if not better, and would expect any other .44 Mag rifle to do similar. Feeding might be a problem with the real oddballs in some rifles, but that's why they're oddballs- because you don't need them much.
My 77/44 came to me used, with a nifty leather stock-mounted 12-loop cartridge carrier. I can have three or four different types of ammo in that carrier and in the magazine, and have ammo ranging from mild loads as quiet as .22s up through near-45-70 factory level stuff. That will take care of a lot of needs.
I'm starting to warm up to the pistol caliber rifle. At least, the .44 Magnum rifle.