@davidkachalon - Strictly speaking, in order to play chords, you have to have your tongue off the harmonica. So that could be one answer: chords. Lol.
But of course TBers play tons of chords using tongue lifting, so we won’t count that one. 
As you mentioned the brightest, thinnest tone possible (super-wide “ee” vowel shape) - like Sonny Terry often did on his whoopin’ tunes on the -4, which Joe Filisko refers to as “icepick tone” is much easier to achieve lip blocking.
Joe can achieve that sound while tongue blocking, but he’s in the rare minority of 100%-TBers that can get a tone that bright, in my opinion. I’m unconvinced that Sonny Terry was TB-ing when he played those notes (though I do think he mostly tongue blocked, especially on his Fox Chase / Lost John stuff.)
The other technique that immediately pops into mind, as you kinda alluded too, you can’t get the kind of articulations that trumpeters call double-tonguing and triple-tonguing: TaKa, TaKaTa, TaKaTaTA.
Oh and I guess another one you can’t does a tongue roll (like rolling your rrrr) like John Lennon does on one of the blow 5’s in his Love Me Do riff. Some people refer to as snoring. (But you CAN get a growly snoring effect while TB-ing using the back of the tongue - it’s just a different sound.)
I’m with you on the pro’s of TB-ing - vamping, splits, split-shakes, slaps, flutters, shimmers - such a rich source of colors and textures. I’m so happy that I’ve devoted so much time to it over the last 5-6 years. And it’s why there’s modules on all those techniques in my Beginner Boss course. It’s a must for authentic roots music and cajun music.
But I think there’s something else on this subject that’s worth noting. When it comes to really fast playing requiring lots of accurate bends I’m not sure that TB-ing can really get the job done (and even more so if you throw in overblows and/or overdraws.)
As an example in the Blues genre, Carlos del Junco is the only player that really comes to mind (and he certainly pushes the boundaries of blues quite a bit!)
But I’m really thinking more in the Gospel and Country genres, like Buddy Greene - I don’t think you can site me a player who plays faster and cleaner than Buddy. I’ve clocked him traveling at speeds of 300BPM, and slowed it down to 20% speed, and his intonation is flawless. He’s an incredibly underrated player, in my opinion. Here’s some links to the kinda stuff I’m talking about:
Do you know any strict tongue-blockers who can play like that? I know some lip blockers who can. (First one that comes to mind is Todd Parrott.)
And you throw in some ob/od’s and it just highlights the point further. Howard Levy’s album Out of the Box is tough for anyone to emulate, but lip blocker is gonna stand a better chance.
I don’t think anyone can pull off Carlos Del Junco’s version of the Chicken while Tonguing. I’m working on it lip blocking, and it’s hard enough!! Check it out:
Now Buddy Greene, Carlos Del Junco, and Howard Levy all do some tongue blocking, and in fact I’ve heard both Carlos and Howard do some pretty fancy tongue blocking stuff. But the majority of what they do is lip blocking, because it’s the only way you can pull that stuff off.
In summary, just like there are some sounds and genres that YOU CANNOT faithfully represent WITHOUT tongue blocking (as I mentions specifically earl on in this long post, there are also some that you cannot faithfully represent only tongue blocking.
Curious to hear other peoples thoughts on this?
I’d love to hear @Corky_Music’s perspective on this subject.