Well, lets see, I've been hunting for over 30 years now and have used all sorts of rifle calibers on deer, moose, antelope, and bear. I shot a moose with a 243 in the shoulder and tracked that sucker for a long way. I also shot a couple with that same rifle caliber, right between the ribs and exploded their heart/lungs. The one with the lungs walked about 50 yards and dropped like a stone.
I have also hit several moos now in the should with a 30-06 in that same shoulder and they folded like a ton of bricks.
The point is that I, myself, me...would not use that light a caliber because the bullet is just too light. My experience is such that I know that if the shot isn't exactly perfect, I am going to have to chase a wounded animal all over the countryside, as it were. My abs are kinda soft and squishy now, so that just isn't my gig anymore.
By reading between the lines in your post, if you had any kind of experience, particularly having to chase a wounded deer after smacking it at 300 yards with a 223 (say with a 55 or 75 gr bullet), you would not have written this post because you would already know your answer.
If it's legal and you want to...go for it, enjoy and get some experience. Better yet, go the the range and shoot a 6x6 block of wood. One with the 223 and then again with a heavier caliber (borrow it if you have too) and compare the two shots. Nextly, read some of the other past posts here on Gunnutz, particularly some of those threads with military folks whom used a 5.56 (223) in battle versus a heavier round.