I'm not familiar with all of the steps they went through to reach this conclusion, but I think the basic idea is that they know energy is quantized, so why shouldn't space and time also be quantized? It is just one of those things that looks as though it ought to follow a pattern. So if space is quantized then what is the size of the space quantum? The Planck length just happens to be a handy size to start with. And of course for time the Planck time would be a handy size.

Bill Gill

C is not the speed of light in a vacuum.
C is the universal speed limit.