the speed of light expressed in units of distance per time, is a dimensionful quantity so it probably doesn’t mean anything to say some theory does or does not predict a value for it. The value is entirely determined by how big you choose your yardsticks and sundials to be, which is arbitrary convention.

It is only meaningful to talk about theoretical predictions of the values of constants if they are dimensionless, like the fine structure constant.

However relativity does suggest as a natural point of view that space and time are just orthogonal directions in a unified spacetime. In this point of view, relativity gives you the option of measuring your timelike and spacelike coordinates with the same yardstick (which you may still choose arbitrarily). And then relativity does predict its value. It’s 1. No units.