That's exactly why .444Marlin and .45-70Gov't outsell .30-30 and .243 every deer season.
Except, they don't. Give some thought to WHY .30-30 is still in the top-10 or better most popular deer cartridges in the US before disagreeing.
"Vista Outdoor, which manufactures both Federal and Remington ammunition, reports that .30-30 ammo is still a big-volume item. The cartridge consistently ranks in or near the top 10 in annual ammo sales.."
https://www.realtree.com/brow-tines-and-backstrap/has-the-30-30-really-killed-the-most-deer
The recoil, muzzle blast, weight of the firearm, and portability all lend themselves to the .357, NOT the .44 - and I'm a Ruger SBH + M77/44 owner and hunter. The 44mag does plenty of damage and that's part of the problem. I want meat, not a trophy. Trophy hunters might prefer a handgun that rips rib meat to shreds but I don't.
Handguns aren't ideal for hunting to begin with. I use a .35Rem Marlin 336T when I have the option. A .30-30 Marlin 336C when I know the range will be flatter and longer. Handguns are for tight quarters, riding, 4-wheelers, swamp brush, and walking trails/fence-lines. The only time a handgun is better than a rifle is chasing coyotes, pigs, and/or wounded deer through thickets, around watering holes, through kudzu, into the palmetto patches... places where a rifle is just too unwieldy. When I do hunt with a handgun deliberately, it's a .357 - either a 6-1/2" Ruger Blackhawk or a 4" Colt Lawman - because they handle faster, point easier, holster more easily, carry lighter, don't over-lead, and the recoil is easier to manage if I get off-balance than a 300gr Sierra out of a SBH - but that's a good load for blinds and tree stands in thick pine. I hunt year-round, mostly on private land, use rifles WAY more than handguns and like to keep a full freezer - which is why I'm not going out this season. Wife says we can't buy another freezer, no place to put it.