Use paste for support material

Ok so I had a thought about support material. Right now only a few support materials exist: PVA and HIPS. I have heard of many problems printing with PVA and it is expensive. HIPS is a bit better for printing, but requires limonene to dissolve, which is expensive and not very reusable due to film from dissolving the HIPs getting on the prints. Plus it requres a pretty hot bed and high temperature, so it doesnt play well with PLA. So I thought why not use a paste extruder and make clay supports? It's super cheap, and dissolves in water. And I think if it was the right formulation, you could get plastic to stick to it (maybe mix school glue into it?). Tell me what you guys think! What are the obstacles you can see?

Paste extruders are big, and from my understanding hard to calibrate. Dual extruders already cut off a lot of printing space. How will it affect the surface quality? even PLA and HIPS leaves a mark. Apart from that... why not?

To be honest, I havn't seen a need for supports that often. Most pieces can be made in multiple parts, or just designed better. Alot of people are very focused on getting usable objects as soon as they leave the print bed, but a bit of post processing goes a long way. Depends what you print I guess