UK luthier, you are right. As you surely must know, it takes a lot of skill to work with hot hide glue, as there is actually less open time to get parts in place before it begins to bond and the parts can't be refit or rearranged as compared to synthetic wood glues. I was wrong to say to was more slow drying. It is less efficient in mass assembly though--especially when building a lower cost instrument, because not only would workers be required to be more skilled to use it, the entire building process would have to be more precise as well. Besides just being easier to work with (and less stinky!) some synthetic glues and even epoxies are used in factory-production guitar making because the builders can work faster and with less precision when cutting and joining parts. The synthetic glues and epoxies do a good job filling gaps without compromising the strength of the joint. Builders don't have to carefully sand braces to match tops, painstakingly fit necks to dovetail joints, etc. like they would when using hot hide glue. Joined surfaces have to be very precise for the thin hide glue to bond. Thicker synthetic glues bonds slightly irregular surfaces more easily so guitars can be built faster and for less less money. I guess in that regard, it's akin to using poly instead of shooting nitrocellulose to finish guitars; poly doesn't always require pore filling, is self-leveling, requires fewer coats, etc., so the guitar can be completed faster (and thus less expensively).
Now, I'm not saying that all builders that use these kind of glues do so because they can take shortcuts and work with axes and butter knives. Not at all. Good builders like Martin and Gibson use it to gain additional open time to work on part positioning (as you pointed out) and more tonal consistency instrument to instrument due to well-joined parts without the incremental extra effort that hide glue would require. But you do see examples of synthetic glues used as gap filler on very low cost instruments, especially before the widespread use of CNC machines.
When the modern Masterbilts were first introduced in the mid 2000's, they were advertised as having hot hide glue joined braces and necks. I don't know whether that is still the case. But Gibson certainly still uses hot hide glue for necks, and even braces and bridges on some models, and will occasionally build an entire guitar with it. Collings uses an "animal protein glue" (said to be fish glue) on some high-end models. Martin still uses it for the high-end Authentic series. Some smaller and boutique builders use it. But as you say, it's not often nowadays used, and when it is, it often comes at a premium.