If our Government feels it is big enough, even with "Ball" bullets to kill big men, why should there be a question with deer?
People are predators. Pound for pound, predators are normally a lot easier to kill than prey. I've seen plenty of deer run off after being hit and/or run completely over on the highway. I've never seen a person get back up from such an encounter, let alone run off into the woods.
We had the good fortune (not sure what else I can call it) of seeing a decent 10 pt die during the 2023/24 season that had an arrow sticking out of it. It was a high lung shot that caught both lungs. It fell over dead standing next to a hot doe at around 10:30 am. It had been shot on the neighboring property the evening prior at around 5pm. The guy who watched it, called the neighbor and helped him retrieve the deer. Generally speaking, even a high double lung shot kills almost anything in less than 30 sec. This was a combination of sub-optimal shot placement combined with a freak occurrence, but we've had similar things happen during archery season in the past. That same year, the hunter who watched the afore mentioned buck killed a nice 148" buck using a 2 blade broadhead. Shot placement wasn't ideal, but it wasn't terrible. There was NO blood trail, and I do mean NONE. He could see the arrow sticking out both sides of the buck as it ran off. I was hunting with him that day, and I moved to a different stand while he and 2 others searched for blood for about 2 hrs with no luck. I stuck a nice doe (heart shot

), so I rejoined them at that point and we started doing an area search. After another hour we gave up the area search, and he and the others went back towards the creek (near where it was shot) thinking it might have double back for water. I took a completely different path back because every deer I've seen pass through that area in the past 40 years has come from one of 2 places, and we hadn't searched the other route at all. I found him laying in the lane way 15' from one of our stands (about 150 yds from where he was shot), dead as a door nail. I tried to back track him to find the blood trail, and only found 3 SMALL drops of blood over the first 30 yds of the trail.
I know there's a HUGE difference between a 223 (or ANY centerfire rifle cartridge), and archery equipment, but you have to admit that a 2" broadhead does cut an awfully big hole. Even a standard 1-1/8" broadhead leaves a hole as big as what I'd expect out of a proper .224 hunting bullet. That doesn't mean that I'm going to hang up my crossbow and only use my Savage ML with a 300gr bullet, but it DOES mean that my muzzleloader provides a MUCH larger margin of error than what I can get with any kind of archery equipment. (BTW, none of us will EVER use a 2 blade broadhead again.... lol).
As far as the army considering 5.56 ball ammo to be "big enough", you have to remember that military small arms are "supposed" to be designed to wound. There's plenty of documented battle field encounters to demonstrate that 5.56 ball ammo does exactly that.