For one thing, we haven't been able to *measure* the speed of Gravity waves inside a Gravity field, much less determine how fast the field itself will travel in order to cover new territory when it is first formed, so that lack of measurement makes Gravity intriguing.
Hey, we know how fast Light travels in a vacuum, so there isn't much mystery or controversy there!
But we know these things in the case of electromagnetism. You've made a geometrical argument why these velocities should be infinite in the case of gravity, but haven't explained why they aren't infinite in the case of electromagnetism. The geometry is the same, so why does your argument fail there?