If the speed of light were infinite, then there would be no time for it to happen. Or anything else of the radio ranges, for that matter. Visible light is a very minute section of the electromagnetic spectrum, encompassing barely a single octave of range. Were the speed infinite, what would stop it? What would shield us against UV, X-ray and gamma? What could?

Light is slowed by the very nature of its propagation through media, in wave-packet (photon) form, which takes on some of the properties of solid matter, and since it does follow wave propagation, then it must have time to create the wave.

Also (and funny you should ask):
Why isn't the speed of light infinite?

Does anything go faster than light?

At the moment, there has never been anything in nature that does, therefore the speed limit has been set.

Bear in mind that science is a self-correcting discipline, so even this is subject to change.

Dan
--ps--
More about light & light speed:
* The Speed of Light Q & A
Scientific American
2001

* Maxwell's Laws of Electrodynamics and Optics
Roberto B. Salgado
Department of Physics - Syracuse University
1995

* How is the speed of light measured?
Philip Gibbs
Mathematics Department - University of California
1997

* Does Gravity Travel at the Speed of Light?
Steve Carlip, Matthew Wiener & Geoffrey Landis
Original by Steve Carlip
Mathematics Department - University of California
1998