Do they? I am not that experienced with lots of 3D modellers being a dumb programmer, but I thought Triangle meshes was what most of them put out?
In any case your understanding is mostly correct.
On Open GL ES and OpenGL3.x onwards QUADS are deprecated. In any case AFAIK the HW always used to convert QUADs to Triangles even before that.SO even when we worked with QUADs they would be made into Triangles prior to rendering.
Switching to triangles on the client side doesn’t actually cost you any more in programming terms. It’s as simple as swapping a couple of Indices or vertices, but it does ensure that all the geometry produced is valid. It’s possible to make QUADs that are not planar, where as that is not the case with Triangles.
I suspect that if the modelling apps you use work with QUADs it’s a convenience to the designer, but it’s actually working in triangles and constructing the QUADs behind the scenes for you… But I am not an expert on modelling software.