Arken I definitely would not use FMJ. Several years ago while fishing at the Russian river for red salmon a guy a few hundred feet up stream of me shot a large sow brown bear with an Ak. 3-4 rounds center mass from 30 feet or so. She ran into the woods svd was later put down by fish and game. This bear was fishing not charging, the guy just got freaked out by how close she was and opened fire. Had she been after him she would have had ample time to do damage as she was still alive several hours later.
The use of a semi auto 308 isn't a bad choice but wouldn't be my first choice. Not even in my top ten. That said I know a guy who lives up in north western Alaska that uses an older DPMS lr308 for everything. Generally with blue box federal loads 150s or 180s. This includes a few big bears, one inside his smokehouse at night from a few feet away. It definitely can work.
My concern is weight and handling. Not to mention I don't generally carry one in the pipe and find a lever or even bolt quicker to rack a shell in than an ar style rifle.
Bears aren't spring loaded behind every tree, if your aware of your surroundings and practice being bear aware you generally will not be surprised by one. Instead of sneaking up on you they generally bluff and bluster a bit trying to intimidate you and can usually be talked out of charging.
I was charged once in a predatory charge. I was sneaking in to a black bear bait site hoping to catch a bear at the barrel when a smaller boar brown bear charged me. Best I can figure was it heard me splashing thru a small spring and didn't know what I was but planned on eating whatever it heard. It came running around the edge of the hill head down all four paws tearing up dirt, I swear it looked like a jack russel chasing a tennis ball. Luckily I was carrying my rifle and was able to light him up with the light mounted to my 375 rum. Between the unexpected bright light and manly screatching he stopped 15-20 feet away. We had a brief stare down until I put a round over its head into a rock wall and he turned inside out sprinting away. It was a pretty nerve wracking walk back out to the truck that night.