oooooookkkkkkkkkkk.... I've been doing a lot of research..... A **lot**.... And I've actually found people that used hot glue sticks to make all kinds of stuff in the the field.
Carved arrow shafts and glued the arrow heads to them
Knife handle popped off, and glued that back on
Fishing pole tip popped off, glued that back on
Joining random pieces of wood together to make random bushcraft stuff.
Etc
Here's what they all said..... It sucks.
The Glue breaks down almost immediately and things start wiggling, it doesn't bond very well at all and in hotter conditions once initially melted, doesn't really ever solidify like it was before. Making it help break down faster.
I'm not going to claim this works all the time, and undoubtedly it depends on the items being glued, but what I've found with glue sticks is that heating the items I'm gluing makes it work better. That is, a cold item will cause the hot glue to cool very fast, so fast sometimes that it doesn't want to stick. So I warm up the item I'm gluing, and it works far better.
How do you do that? In my shop, I'll warm up the item with a heat gun or maybe put it next to a light bulb in a trouble light. Out in the field, it's a bit tougher but not extremely so--warm up the item with a butane lighter or a candle; hold the item pieces next to the flame, not above it, and warm them up.
The other thing about glue sticks is that they're somewhat pliable. You don't end up with a hard unmoving bond--it's slightly flexible. If the glue repair requires some flexibility, it's fine.
Like anything else, it has to be the right tool for the job. I don't have any of these in my BOB, but I think I'll toss a couple in--and maybe a couple in my car kits as well. I have some super glue tubes in my BOB--maybe I'll toss in some Gorilla glue too if I can find the small tubes.