As I understood, Protoss are the most advanced race of all (as long as we talk about tech), and remembering SC1 you could mind-control some terran medics and get your zealots, templars and dark templars healed. However if you steal an SCV you cannot repair your damaged structures/buildings. Thats OK because are different technologies. However, since Protoss are the most intelligent, i cant understand why they dont learn:

If their buildings and units are so expensive... Why not fix it?
If Protoss life is so preciuous... Why not learn from medics?

Im not thinkig on have protos medics, but why not to have a building which allow protoss to recover some HP or some Psi-like hability (spell) which allow Protoss living units gain a low hp regeneration at cost of loose all shield while healing? What about fusion two havy damaged units to get a new one with all HP and shield?

While it does make sense form a real-world/lore perspective, I believe the reason that the protoss cannot heal is for balance purposes. They would be too strong. The regeneration of the Zerg (shields) combined the the healing of the Terrans (HP) = overpowering.