Why do we associate the speed of time with the speed of light? Is this even valid assumption?

Yes.

A better name for "the speed of light" might actually be "the speed of time" or "the speed of information transfer".

It's a mathematical limit and you can derive it using pretty much anything, not just light.

As an object goes faster, it experiences time dilation, length contraction, etc. The "Speed of Light" C is basically the point at which all of these things reach either zero or infinity.

It also "just so happens" that electromagnetic waves (such as light) travel at exactly this speed in a vacuum. They travel that fast because they travel at the maximum possible speed, and that happens to be the maximum possible speed.

It's like if you always traveled at the speed limit because you didn't want to break the law, and we called it "triplesex_ speed", but really it's just the maximum speed that anyone would go if they didn't want to break the law.

Except in this case it's not just a law- it is (to the best of our knowledge) physically impossible to go faster. It's not just that we haven't seen anything go that fast- it's that going faster than that doesn't even really make sense theoretically - for example, it would result in time-travel (this has to do with the fact that the order in which events happen and the speed at which time passes is different to different observers depending on the speed at which you're traveling).

It is not an assumption, in layman terms: "speed of light" is a bad name. It is actually speed on interaction. Top speed of any interaction. Everything which isn't slowed down by mass has this speed, like light.

I’ve heard it explained as the speed of causality (that is, the maximum speed at which cause and effect can occur) and, like you say, anything without mass to slow it down, like light, will travel at that speed. It’s the propagation delay for quantum states or whatever.

They do blue or red shift in response to gravitational gradients and the like.

Yes, but from your point of view, not theirs

Ack, can't believe I missed that! Still, the same question could be asked for other particles that can be split in the same manner ... if such particles exist.

I have never though about it but that makes absolute sense.

Thanks for pointing that out.