The picture appears now to be a little more complex than previously supposed, see update to other Answer in What are the different grain directions, and how do they affect joint strength? and the Comments that follow.
In practice end-grain glue joints are typically weak for various reasons discussed in the follow-ons to that iconic video. Even in a low-stress use like a smallish picture frame it is still advisable to ensure your mitres are pretty much perfect, you glue and clamp with particular care. And by all means reinforce the joint if you want to future-proof it against unexpected strain.
Various reinforcement methods are available for mitres, the simplest (e.g. nailing or pegging) take almost no extra time, and some of the more involved ones (e.g. keys) look good while adding lots of strength.
it sounds like the consensus is that gluing end-grain just doesn't work well.
It has long been acknowledged to be the weakest joint. However, that doesn't mean you can't or shouldn't do it, ever.
The issue is actually whether it's strong enough, not strong per se. In a picture frame for example a simple glued mitre is not considered strong enough, and for good reason because the mitre would be the only joint responsible for holding the piece together, the glue surface area is small and the combined weight of picture, matt and glass can be considerable. And note the orientation of the joint faces to the load — pulling it directly apart. Failure in this situation could be considered likely, not just possible.
But if the mitre is at right angles to the load, and the weight it must bear is small (e.g. the weight of just the pieces of wood themselves, as in a crown moulding), then a simple glued mitre could easily be sufficient.
To be honest though, given how easy it is to reinforce the mitre, even a single staple across the joint adds a lot of strength, it hardly seems worth taking the chance that it might separate on its own. I should also mention corrugated fasteners here, although they're looked down upon by many woodworkers as being crude they should be considered for this as they stabilise the joint immensely.
Is this true for all glues – even epoxy and CYA?
CA/superglue is a particularly poor woodworking adhesive anyway as it is too brittle to deal with movement, and it's poorly suited to highly-absorbent materials which of course end grain is (neither of which stop it being sold for this purpose).
Epoxy on the other hand is a much stronger class of adhesive and it deals better with unusual surfaces or textures. To glue end grain best with epoxy you would want to pre-wet both joint faces with the adhesive and then apply additional glue to the surface before bringing the pieces together. There is a problem however, as strong as epoxy is it is not a good thin-film adhesive (thin like woodworkers want, nearly invisible) which is why you don't want to use very firm clamp pressure with epoxies. So to be at maximum strength the mitre joint would end up quite visible.
It seems like there should be a way to seal the end-grain to prevent it from (excessively) drawing in glue, while still preserving the surface area and characteristics that allow wood glues to work effectively. Are there no established processes for that?
The absorbency of the end grain was identified by craftsmen as the problem and sealing of the end grain prior to final glueing to fix it was theorised a long time back, possibly before the 19th century. Certainly by then there was mention in woodworking handbooks of 'sizing' the end grain (painting with thinned glue) prior to application of the full-strength adhesive to the mitre and then bringing the joint together. Done correctly this does create a far stronger union between the mitred pieces than otherwise, but even with that it is not as strong a joint as is sometimes desirable. Bear in mind the context here: the strength of other joints in woodworking is as strong as the material itself, which is quite a high standard to meet.
Using modern PVA-type woodworking adhesives if you want to avoid using any kind of additional reinforcement then this is the method to adopt. In bullet points for clarity:
- The glue for sizing is normally slightly thinned; by how much is open to debate, but it seems likely the absorbency of the wood species should be the deciding factor.
- The size is painted on the end grain and left to partially dry.
- Application of full-strength glue and clamping.
The drying time for the sizing may be anywhere from 15 minutes to an hour, depending on wood species, the glue used and local conditions (temperature and relative humidity).