Because the basic understanding of physics is that all particles move at constant speed c in spacetime; the proportion of their speed that is happening in the three spatial dimensions is determined by their mass. So, any particle's speed through space is a fraction of the "speed of light" c; the higher its mass, the lower the fraction.
The other items I mentioned are then caused by the speed of these particles. The speed of sound in a medium is determined by how fast particles collide into other particles in the medium. The speed of the earth around its axis (the length of a day) is determined by the speed of the particles making it up in the warped spacetime of the earth's gravitational field. The speed of chemical reactions is also limited by how fast atoms and electrons move and can interact with each other.
The length of a day, at least, is unrelated. There was a big splash in the news not long ago because it was determined that the length of Earth's day was changing and we might need to change it by a second.
Venus has a much, much slower rotation on its axis, but Mars is almost the same.
I doubt it was a big splash of news given that leap seconds have been a fairly routine thing for quite a while. Lately there’s been talk about a possible negative leap second, as Earth’s rotation speed has been increasing for a few years now. Many things can have a measurable on Earth’s rotation, including dynamics of the molten outer core, earthquakes, ocean currents, and melting of polar ice caused by the climate change.
Even before we invented precise enough clocks that there was any need for leap seconds, we knew that Earth’s rotation is slowing down due to tidal drag – the moon is literally robbing angular momentum from Earth, and getting farther from Earth in the process. Back in the Cambrian, day length was around 21 hours. Shortly after the formation of the moon, 4.5Ga ago, it would have been only around five hours, assuming the giant impact hypothesis is correct.
Leap seconds are just an imperfection in how we measure days. The recent splash was largely because it was being blamed on changes due to global warming.
In any case, it all goes to my point- the Earth's mass has no bearing on its rotational speed.
I've read that C is really the speed of causality, and that electromagnetic radiation is really a disturbance in the EM field that is propagating along a path. A photon is really information about a prior event, that caused the disturbance i.e. emitted the photon, propagating across the EM field at the rate C. Likewise gravity, the strong force, and the weak force are also propagated at the speed of causality. E.g. if the Sun suddenly doubled in mass for some reason, it wouldn't just take eight minutes for us to see the change in EM radiation, it would also take eight minutes for us to feel the gravitational change.
The whole bit about the physical laws being the same follows from that, and the assumption that there isn't any way to transmit forces across spacetime except through transmission of causality.
The other items I mentioned are then caused by the speed of these particles. The speed of sound in a medium is determined by how fast particles collide into other particles in the medium. The speed of the earth around its axis (the length of a day) is determined by the speed of the particles making it up in the warped spacetime of the earth's gravitational field. The speed of chemical reactions is also limited by how fast atoms and electrons move and can interact with each other.