So it turns out that the reason why Discovery doesn't (and can't) tie in to Star Trek's continuity is that it's being produced by Paramount & Bad Robot. After Viacom split into CBS Inc. and Paramount, the license to televised Trek and the first 10 films went to CBS, while the license to produce more films stayed with Paramount.
That's why the JJTrek films had to take place in an "alternate reality" -- they legally couldn't use canon designs, just the names of characters, places, etc. The "melted in a microwave" JJprise came about because they weren't licensed to make a version that didn't look stupid.
Same with Discovery -- it's being produced on the Paramount/Bad Robot version of the license, not CBS's, because Paramount wants to get the most out of the license and not let it lapse, and CBS wants something to launch their streaming service with.
All of that is perfectly understandable and I have no problem with any of it. Still sore that they're telling us it's set in the prime timeline when not only is it obvious that it isn't, but for those "back stage" legal reasons, it can't be.