Academics do love their new fancy stuff. Here's the thing: elliptic curve cryptography is not particularly new anymore. I'd buy this neophilia argument if it were concerning pairings, ideal lattices, or the stuff people are doing with these nowadays (FHE, obfuscation, etc).
Elliptic curves were proposed, and have since been studied in the context of cryptography, in 1985. They're 30 years old! For comparison, finite field discrete-log Diffie-Hellman is 38 years old, and RSA is 37. The latter have been severely beaten down in the ensuing decades that followed, whereas elliptic curves have stayed (modulo special cases, but those also exist for DH/RSA) resistant to every non-generic attack so far. I would say ECC has a better track record, and could be considered the conservative choice.
It could be argued that the underlying problem, integer factorization and FF discrete log, has been studied for much longer than the ECDLP. Maybe. Some basic algorithms go centuries back, but I would argue that the field has only seen real progress starting in the mid-1970s, with CFRAC and Pollard's algorithms. It can be counter-argued that elliptic curves as a subject have only existed for around 100 years, so they are still underdeveloped. Again, maybe.
There is indeed a new wave of interest in elliptic curves, and it is still fueling many publications every year. But these are mostly performance engineering at this point: Edwards curves are not fundamentally different from what Miller proposed in 1985, as far as the ECDLP is concerned. I would not recommend the wonkier stuff like GLS/GLV curves, though, nor curves over extension fields or of higher genus: that would be too neophiliac, even for me.
(I realize that I'm not gonna change your (or probably anyone's) mind, but you make it sound like elliptic curves are much more of a novelty than they really are. I don't disagree too much about the AEAD vs CTR+HMAC issue.)