A mod called Elytra Slot (called Curios Elytra in 1.16) adds the ability to place the Elytra in the Curios:Back slot, and use it as normal with other pieces of armor. Some other mods including Iron Elytra (1.16) and Netherite Elytra (1.18) Both are compatible with and work in the same way as this mod.

I have tried adding the Curios:Back tag to the Tarantula Hawk Elytra manually, and although I can place it in the designated slot, it does not function as an elytra.

This seems like something that wouldn't be too tough to implement, seeing as those other mods I listed have done it, and as long as it only takes effect when Elytra Slot is installed, it wouldn't require Alex's Mobs to have any extra dependencies.

I was just thinking about this! I would love to see this in game. Additional, compatibility with Aileron would be nice

Same issue here. I wanted to use this elytra with the Elytra Slot mod, and I've even made a separate Curio slot that only takes elytras.
But alas, the Tarantula Hawk Elytra can't be used when in the Curio slot, it doesn't even get rendered.
Please, can we get this compatibility feature?