Set necks have been the "right" way to do it for hundreds of years. Bolt-ons were a Leo Fender idea (pretty sure) from 1948.
The amount of engagement surface in a set neck joint is substantial and on multiple planes, so there's a LOT of glue in several directions.
It's ridiculously strong compared to a bolt neck. I have never even heard of one failing under any condition short of catastrophic. I've handled bolt-on instruments where the neck pocket is poorly made, and the neck shifts position easily, throwing out the tuning and intonation. Never happens with a glued neck. Have you noticed how many basses these days use 5 or 6 bolts instead of four? To make the connection stronger and more stable. Because bolt-on necks aren't perfect.
When guitarists and bassists used to smash their instruments on purpose, the neck bolts would often give out early and the neck would stay intact until hit again separately. Trying to smash a Gibson wasn't done, because the neck joint was too strong. (And were too expensive, I bet).
Google around for photos of set neck instruments under construction. It's nothing like what you would get by gluing a Fender neck to the body.
There's some old-world knowledge and craftsmanship involved that gets the job done correctly.
And as mentioned, quality glue joints are much stronger than the surrounding wood. This is why laminated necks are so much stiffer than 1 piece, for example. I believe a set neck is every bit as strong as a neck-through, for all practical purposes. You would have to be seriously trying to kill a guitar on purpose to have a problem with one.
The headstock breakage on Gibsons is well-documented. It's a design flaw related to the direction of the wood's grain at that point.
The solution that many other companies now use on similar designs is called a scarf joint. The headstock and first few inches of the neck are made using wood whose grain goes in a different direction than the rest of the neck. The 2 parts of the neck are glued together, and a scarf joint is not going to fail in any way.
In the early days, airplanes were made of wood. Much of the construction used glues rather than bolts because it IS stronger. People bet their lives on it.