If the right filament material is available, it seems practical for dentist to 3D print temporary crowns. Multiple images of the tooth to crown could be used for a 3D scan. Custom software or settings would probably make the software finish in less time. A 3D-printed temporary crown would probably take less work to get it to fit properly. Anyone know of development to do this? This probably would take a series of clinical trials to get FDA approval.
You ask about "filament", so I assume you expect fused-filament technologies. These are however not accurate enough, besides being prone to gaps and crevices which are problematic in crowns. The smallest viable nozzle, 0.2 mm, is still too rough for that.
Dental 3D printers need to be very accurate, so the most common technologies used are stereolithography (SLA) and digital light processing (DLP).
Crowns can be made using resin printing. It is possible to use also CNC machining of porcelain, but it's not part of 3D printing.
More info can be found on https://all3dp.com/2/dental-3d-printing-guide/