I received some conflicting answers on this:

Should judges run to judge calls, perhaps if the judge call was unanswered for some time because of judge shortage, or if they are in a hurry, rather than walk?

One opinion is that we shouldn't because it's unprofessional, perhaps dangerous.
But still others do run. It does get you where you want to go more quickly and perhaps shows your dedication?

Running judges can cause panic and fear. When people of importance run, mob mentality can cause more trouble than its worth.

If you have to be quick to get to a table walk fast. I'm sure the difference of 20~ seconds is not going to matter 99% of the time. There's no need to run.

I'm curious if you have actually gotten conflicting answers or not. I've
never seen anyone advocate running on the floor. I've seen people do it at
times, but that behavior is usually corrected.
You should move quickly to calls, but not run. Not only could it cause
panic, it can also be dangerous because the judge may run into players, etc.

Moving quickly shows the players that you are trying to get to them and the
time saved by running isn't worth the hazards.

Breaking a sweat or being unable to catch your breath at the table are both
pretty unprofessional.

If the number and distribution of judges is such that the difference
between running and walking briskly to a table is going to be significant,
you should solve that problem, rather than try to patch it by doing wind
sprints.

I agree with Nick on this.

The little time saved isn't worth setting a bad example, or the risk of injury to yourself and others should someone suddenly enter your path.

I'll wrap it up very simply: no, do not run to a judge call.