Both the 243 and the 300 Mag will kill deer effectively with proper bullets and placement.
Deer drives and 22 LR???? Deer drives are mostly running shots and hardly the place for 22LR. Also not legal anywhere that I am aware of.
As to people that have marginal hits improving the odds with large calibers I've never really observed much of a difference until you get outside of normal combinations. A poor hit with a 243, 7mm Mag or a 300 Mag is still a poor hit.
The one prime example is the land owners bother-in-law. He flew in from NY every year. He used a 300 Weatherby Magnum and lost lots of deer using 165 grain bullets. He switched to 125 grain Nosler Ballistic tips at a little over a chronographed 3,600 FPS. He stopped losing deer mostly but the best way to describe a deer hit with that combo was to compare it to a fox hit with an explosive 220 Swift bullet. It would literally blow most of the off quarter away and it didn't matter if it was the front shoulder or the hindquarter. Gut shots left cantaloupe sized holes that they did run away from. Not much useable meat with that combo. The 125 grain was way more destructive and explosive than the 165 grain. You still could shoot a leg off or a nose off and still lose the deer. Yes he was a slob hunter but he was family and I wasn't. The landowner didn't care he just wanted every deer gone.
Didn't realize we were talking about grizzly bear. I have one of those coming up. If it's a spring hunt I haven't decided if I will take my 375 H&H or my new yet unfired 416 Rigby. Thinking my 416 Rigby with Barnes 350 grain TTSX BT at about 2,550 should do the job nicely. If it's a fall hunt I may use my bow. Either way the .243 is staying home.
That being a said a very good friend is the owner and operator of a Grizzly bear and Salmon Guide service in Alaska. He did have one client use a 6.5 Creedmoor to take a 9 foot Grizzly. He carries a 375H&H as a stopper rifle. It was not needed. On fall hunts he does allow archery from tree stands. He has stopped several bear charges in the 35 years he has been guiding.
Back to the subject at hand if I strictly go by numbers of almost lost deer and or challenging recoveries that I personally experienced the .270, 30-06, 338 Win Mag and the 375 H&H would be found lacking. Nothing is further from the truth. Total number that I've killed with the 270, 338 Win Mag and 375 H&H is only about a dozen and half yet each one of the calibers produced my most challenging recovers due to using bullets designed for much larger game. If I would have been using my 243 none of those three would have made it 30 yards.
With the 30-06 I mostly used that from 12 years old to 16 years old and shot selection wasn't the best. That rifle got traded for a Browning Sako 243 that killed a lot of deer without a loss and it made a lot of money killing coyotes in the mid-70 through the mid 80's. I tried a FMJ's loaded down to limit fur damage but in the end I lost more money to not recovered coyotes verse additional hide damage. Lost to many with FMJs and varmint bullets did way to much fur damage. The same 100 soft points anchored them well and fur damage was mostly repairable.
1976 was the first year I used the 243 for deer. It didn't start well. We had been hunting that land since 1970 and while you had to look for mule deer in the hills no one had ever killed a mule deer in the heavy wood. I had my whitetail buck tag, permission to fill my dad's whitetail buck tag and permission to fill one more whitetail buck tag. I saw three very nice bucks coming my way. Mule deer required a mule deer tag which none of us had. Three shots and three deer on the ground all mulies. I didn't have a clue until I started gutting the first one. The largest was 26" inside spread. None of the 25 or so other hunters had a tag for mule deer but two of the adjacent land owners had gratis tags that could be used for anything however that was for their land only. They actually wanted mule deer since they are larger bodies and they just went into the fall sausage making. The bigger the better. The third I had to drive about 10 miles to get some who would tag it and yes none of that was legal.
Party hunting was also not legal in that state but if you wanted to hunt on that land you party hunted. The land owner hated deer and want them all gone. If was a noon opener on Friday and all day for the following two weeks. We would set in the stands all Friday and until 9:30 in the mornings. After that is was 100% deer drives. I killed the three mulies on Friday and nothing on Saturday. On Saturday they had a drive and one of the posters missed a bunch of deer. On Sunday they put me in that tree stand. Five shots with my 243 and 4 bucks and one doe on the ground. Eight shots and 8 deer on the ground in three days but I guess if I would have been using a bigger rifle I would have done better.
The 243 will be around for as long as the politicians allow it.
To the OP's question yes the .243 is losing popularity simply because there are a many more choices currently. The 243/6mm caliber is graining greatly in popularity for both competition and hunting. Most of that is coming from 30 caliber shooters. Other than Palma not many using 30 calibers for long range competition anymore. Most are using 6mm, 6,5 or 7mm. For the ultra-long range 338, 375 and 416 calibers of choice. Same is happening in hunting.
Just like the .243 the various 30 cals. are not going away any time soon for hunting and they still are just as effective as they always were.