From what I've been reading bears in that region feed mostly on fish. Bear hunting with a 40 lb recurve... blush I'm sure it could be done. Even with DIY deadfalls Rambo style and whatnot - in theory. Doing it solo in unknown terrain sounds a little risky though so I wouldn't blame the contestants for not trying.

Historically, bear (and also boar) hunting in Europe was often done with a heavy lugged spear, but usually with a pack of trained hunting dogs and a number of well armed assistants for backup. It was considered the riskiest and manliest form of hunting, practiced more or less exclusively by the noble classes who were trained almost from birth in hand-to-hand combat and military skills. I don't think anyone on "Alone" had that kind of background.

Hunting with improvised weapons sounds pretty cool but it's not exactly easy. I've made a few bows in my time, some good enough for hunting. But it takes a lot of time and effort. Very easy to screw up, especially if you try to rush the process.

Making a bow that hits hard enough is one part of the challenge. Accuracy is an even bigger concern. It's remarkably difficult to make arrows reasonably matched in spine and weight without access to a good workshop and first-rate materials. Meaning that your DIY bushcraft arrows will be all over the place. Besides, even with good equipment and quality arrows serious accuracy with a traditional bow is hard to achieve unless you practice constantly. Many people have a hard time keeping their arrows within a pie plate sized target at 20 yards. Hardly good enough for small critters like rabbit or squirrel.

A good compound bow is a different story. I feel confident that I could take just about any game in the Northern hemisphere with my 70 lb Hoyt. I can shoot it pretty well and it hits like a laser with good carbon or FMJ arrows. With a slow 50 lb recurve at half the kinetic energy, not so much. Even less with a DIY bow and arrows hastily crafted out in the field. And I'm simply not proficient with a sling or atlatl (not that I haven't tried, it's just beyond my skills). I'm sure there are people out there far more adept with primitive weapons but for most of us it's not a particularly realistic option. YMMV...