I haven't used many templates yet, but I'd probably go light on their use. I'd agree that the fiendish dire axiomatic half-celestial undead half-pixie owlbears are simply asinine. How the hell can one logically come up with such an unlikely combination?
Using say fiendish/celestial/axiomatic/anarchic/elemantal templates on a creature (and only one at a time) is ok. Hell, you can just summon the suckers uup with the
summon monster spells. The occasional half-fiends/celestials or whatever aren't too overboard either, if used sparingly. But dumping a whole bunch of templates nilly-willy on a monster for the sake of raising CR just seems dumb.
I have however, frequently added class levels to monsters. Sure I use normal orcs, goblinoids and kobolds, but leaders always have class levels. I used to to that in 2e, making orc leaders stuff like 3rd level fighters instead of just big orcs with 3 HD. When humanoid opponents have classes and levels like the PCs, they become more dangerous.
And besides, I never tell the characters exactly what they're fighting. I describe what they're seeing, and always play up the most threatening stuff. Sometimes the players will eventually guess it, but by then, it's too late.

Besides, they never know what I'll throw at them (like the mimic with an attitude they encountered recently), so they stay on their toes.
Common humanoids, like goblins, kobolds and such will be described as such, but classes and levels are never mentioned. Even such weak monsters can make an interesting encounter, like the time I had some kobolds sic their pet komodo dragon on the party, while remaining behind cover and sniping at the PCs with missile fire.