There is a text based file format for models. It's called OpenSCAD. It's also much more information compacted than a mesh model file like STL - e.g. in OpenSCAD you describe the curve, in the mesh file like STL you explicitly state all elements of it.

It's just gimped to the point that you can basically only use it for hobbyist projects, anything reasonably professional looking is using STEP compatible files and that is much more complex to try to emulate and get right. STEP is a bit different - it's more like a mesh in that it contains the final geometry, but in BRep which is pretty close to the machining grade, while OpenSCAD is more like what you're asking about - a textual recipe to generate curves that you pass into an engine that turns it into the actual geometry. It's just that OpenSCAD is so wholly insufficient to express what professional designs need it never gets used in the professional world.