A simple table wouldn't really do the job, since within a class, there's so much variation.
I am more optimistic, and say that it would be possible.
Yes there is a lot of variation within each class. Trying to cover a large variety doesn't have to be a target of such table.
The table can just aim at estimating the CR of an NPC designed for battle. As you say, a
diviner is not supposed to be as good in battle as an
evoker. But that also means, that you'll rarely require the PCs to defeat a diviner in combat, and if the BBEG is a diviner, maybe the last fight against it is not even supposed to be the toughest part. Similarly, give me the CR of a Rogue which is built for fighting, not a Rogue built for trapfinding or a con-artist. So just give me the CR of an
evoker or standard Rogue of level X, and it'll be already useful!
Then if I still occasionally want the party to face a trapfinder or a diviner in battle, I'll have to expect it will be easier, or I'll buff it up with a few additional levels.
Still, during the combat fight even the trapfinder and the diviner could just fire off all their daily weapons. The diviner could have 90% of divination spells in her spellbook, but remember that with 5e spellcasting rules, it might be enough for her to have
Magic Missile and
Fireball prepared, and still be able to be fairly effective at combat, even if all the rest of prepared spells are divinations. So maybe the CR wouldn't even be that much lower than the evoker's.
My point is that the
variety really shows up in the long term (i.e. when you have investigations, exploration, problem-solving etc... involving all 3 pillars). In the course of an adventuring day, different PCs will shine in different pillars. But in the short term of a single fight (which is what the NPC will do), the differences are smaller. Barring extreme cases* of course, for example if the NPC
only prepares divination spells.
*bottom line: it seems absurd that just because it's impossible to adequately cover the extreme (and rare) cases, the game gives up on covering the common cases. The MM chooses to provide a CR6 and CR12 sample mages, maybe these are considered to be the most common cases. Well that's really too little IMO!
Add to that the idea that bounded accuracy should mean that getting the CR wrong by a couple of points shouldn't change much, and I say the whole 'CR by class level' should be doable.