How come they used to ground one leg on a delta system in some applications.

In a nutshell:
One leg would be grounded for safety reasons.

A short circuit in grounded delta systems will open short circuit protection devices.

Obviously, an open fuse will shut down power, and the equipment being served by that system.

An ungrounded systems are used for operations that could be affected by an open fuse. System will continue to operate. These systems will have some sort of indication of a short circuit, and allow the problem to be repaired when possible.