Even a single transparent mesh can have these issues, depending on its shape and self-occlusion. Mostly this particular model is difficult because its entire frame is slightly transparent. Compare these two renders, where I change the frame’s material mode in Blender from “Alpha Blend” to “Alpha Hash”:
Alpha Blend
Alpha Hash
EDIT: Note that these were taken in Blender’s Eevee renderer, which is a better approximation of a realtime engine’s capabilities.
That works better, but unfortunately you can’t export “Alpha Hash” from Blender. There may be other workarounds possible by splitting up or combining meshes in certain ways, but I don’t know what they would be.
It might be worth filing a feature request on three.js for something like an “Alpha Hash” or “Alpha Dither” mode. We’ve discussed it a few times but I don’t think there is an open feature request.