Hi folks,
I have access to and use photo-polymerizing resins every day. Ask your dentist and he/she will have a pile of it, used for white dental fillings. The concept makes sense, however the implementation does not. There are many reasons (already mentioned in this thread) that are technical challenges that need to be over-come.
For one, the energy for photo-polymerizing resins has to be high. In the dental office, they use a specific intense UV blue light. Theoretically you could partially cure the resin with a weak light and then place it in a curing oven (which has intense lights) to complete the process once the soft structure has been weakly bonded together. But your object may collapse or distort if it is very fine.
Other resin-based printers I've seen use a laser to cure the resin from underneath, usually a blue one of the proper frequency. Mirrors deflect the laser beam, just like if you were doing a laser light show but drawing on the bottom of the tank of resin.
Theoretically you could also do this with a matrix of tightly-packed bright blue LED's, light up the LED's to form the cross-sectional shapes of the object you want to print, then lift the "printing ceiling" (as it prints upside down) and cure the next layer, and so on. Each cure bonds on to the preceding layer above it.
There is one more thing.... something called the "oxygen inhibition layer". When curing resin, the surface that is in atmosphere will still retain the ability to have new resin bond to it. That allows you to add more material and incrementally cure it. If you take a solid block of resin that is already cured and has been polished or cut, you will not be able to cure new resin to it (there is a process needed to prime it again).
So the resin printers I have seen all find a clever way to create an oxygen inhibition layer at the bottom of the tank. Usually there is a membrane that is small enough to allow air molecules to interact with the material yet prevent the resin from pouring out.
See this:
https://3dprint.com/51566/carbon3d-clip-3d-printing/https://youtu.be/VTJq9Z5g4Jk