Back to hunting, the 77g 5.56 certainly has its place, specifically smaller static animals at shorter ranges. I would not classify 5.56 as an “all around” big game cartridge as indicated by the thread title since there are so many other great options.
I think what most people miss in this discussion are factors relating to shootability - you can't just take the cartridge and math it out in isolation of that. Context and human factors matter immensely.
Yes, there are plenty of amazing cartridges out there - but how many can someone shoot 200 focused, careful rounds out of in an afternoon, without developing a flinch or breaking the bank? Now jack that up to 5000 rounds a year. How many heavy recoiling cartridges will allow someone to shoot from a dozen different improvised field positions without smoking their own forehead with their scope?
What you get out of 5.56 is excellent shot placement, due to practice, familiarity, and exceptional knowledge-based experience of your rifle.
Sure, you can move up to things that have similarly low recoil, like .22-250, 22Creedmoor, .243, 6CM, etc, but how much of that can you shoot on your personal budget, compared to .223? There's no replacement for experience - double the cost of ammo for most people, and you halve the amount of shooting most can do.
Psychology matters here, too - over the years, I've become pretty convinced that a huge part of "buck fever" or target panic comes from not knowing your weapon intimately. Not knowing you can smoke that animal from any number of positions at all sorts of distances, because you haven't done it in practice. That angle, that brush, that distance, that wind, those shadows, that dust, that snow. The only way to get that is with practice to the point where you've done it or something very close in practice hundreds of times. And you're just not going to get that with a heavy recoiling cartridge. And - the honest threshold for flinch or recoil-anticipation is a lot lower than most people will admit.
