Elemental is one of those words with two definitions: the “real” one and the “D&D” one. The word elemental comes from Paracelsus; we get our words gnome, undine and sylph from him. And that’s the thing to focus on here: his nymphs, sylphs, gnomes and salamanders are beings who wear pants and eat sandwiches; though invested with elemental powers they have biology.
D&D elementals are undifferentiated masses of their elemental substance taking on (very) vaguely human forms. No pants, no sandwiches; if you’re a ten foot tall wave, you do your summoner’s business and then go home.
But luckily, D&D has both a monster named elemental, and a monster type named elemental. The other inhabitants of that type — gargoyles, salamanders, water wierds, invisible stalkers — are much more interesting. We also have the various genie-type monsters, again, much more satisfying wearers of the elemental mantle.
If it weren’t for its effects on the summoning spells, I’d actually split the creature-named-Elemental apart from the Conjure Elemental spell. Consider: if I did, the Conjure Elemental spell would never be worth it for water types. At CR 5, you can call salamanders and xorn; at 6, galeb duhr and invisible stalkers. Then a great void. Nothing water typed. The only whole-number-CR’d water-typed elemental is the ‘weird at CR 3, in the gap where conjure minor elementals can’t reach them, but conjure elementals isn’t worth it. Do I care? I’m not sure. It makes it clear that the purpose of the elemental-typed monsters is to feed the conjure elemental spell; having left the salamander and xorn behind, I don’t feel too much shame. Contrast with conjure celestial, which basically gets you couatl or a unicorn at 9th level.
I could say that the genasi was enough of an elemental/humanoid hybrid, and allow the spell to summon a CR 5 gladiator or master thief/CR 6 mage (?!)/CR 7 nothing/CR 8 assassin/CR 9 champion. I guess. Unsatisfying, and what are all of these name-level “heroes” doing, awaiting the call?
Since we need elementals at levels 7, 8 and 9 anyway, maybe I should aim there. An easy low-hanging fruit is the CR 8 Hydra. Just pull it over: poof, water-type monster! It has the same alien biology as the xorn. Everyone likes cryohydrae/pyrohydrae/etc; I don’t feel any shame over elementally inflecting an elementally aspected monster, so that’s fine. I might also let you call the CR 7 stone giant, CR 8 ice giant, CR 9 cloud and fire giants.
Okay, so it could be done. Is it worth it? I mean, removing content just feels off. But if I make the creature-named-Elemental a construct, it isn’t an elemental-typed creature, so it isn’t a legal summon target. It’s like making flesh golems animated by undead spirits: it makes them vulnerable to turning.
I think it’s worth it. Who are the 5e MM authors to tell us that a creature made out of mud, animated by magic, is summonable instead of constructable?