The giant spring didn't propel the bomb. The thing is a spigot mortar. Spigot mortars were made in various sizes, some quite large.
The propulsion cartridge is inside the tail of the bomb. When the trigger is pulled, the "bolt" hurtles forward, and the spigot enters the tail of the bomb, and strikes the cartridge. The bomb is blown off the spigot, while at the same time the spigot is blown backwards, compressing the recoil spring, and re-cocking the "bolt", ready for another bomb to be laid in the trough.
Hand launched rocket launchers were an option being developed about the same time. US with the 2.36", Germans with the 88mm. Developing rocket motors that were safe and reliable in different temperatures was a bit of a challenge. The PIAT projectile used the same shaped charge technology as the rockets. It was a primitive thing that served its purpose, but became obsolescent quite quickly.