If light doesn’t experience time, how does it have a limited speed?
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It’s just something that’s baked into the universe itself. Like the current top comment says, it would be better if we actually referred to the speed of light as the speed of causality. Light is just the top racer who is stuck at that speed limit.
As for it being baked into the universe, it’s a bit like asking why if you walk in a straight line on a sphere, you end up where you started. That’s a feature of living on a sphere. The speed of causality is a feature of living in our universe.
As to why this speed is what it is, that has to do with the complex shape of the universe, similar to how the diameter of the sphere will determine how long it’ll take you to get back where you started on your trip across the surface of the sphere.
The time part of OP’s question is stuck in some confusion about the unitary nature of space-time and the mathematical singularity of infinity. Easier to say that to ‘experience’ time requires a conscious observer for the question to make any sense. That in turn will take you to Einstein’s wonky thought experiments with time dilated observers. Time will pass normally within every observer’s frame of reference of itself (even near light speed) but will look very weird when they observe something else. Like a very slow observer (us) observing something very fast (light).
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