When you need a weapon, any weapon is better than no weapon.
Those of us, like me, who disagree with you, do so not substantively based on your principles, but because carrying a knife doesn't seem to sufficiently back them up. If you happen to be at some sort of a gym where there are no free weights or anything that could possibly be used as a weapon (seems doubtful to me, but I'll grant you the premise), and you are actually legitimately concerned about the possibility of a gym shooting, I submit that the intelligent course would be to carry a gun, unless that's for some reason not an option. Most of the people I've teasingly referred to as gym ninjas are arguing that they're going to carry around a knife for self-defense reasons, and that said knife is "of course," going to be a lightweight folder. I think you and I probably agree that's a rather poorly thought-out premise.
I tend to think that the whole carrying a knife for self-defense reasons is somewhat inane, given that most states prohibit concealed carry of knives that are any kind of useful length, and frown on open carry, so most of the "self-defense" knives that actually get carried are very poor substitutes for many other things that CAN be carried concealed or openly. In fact, here in Colorado, a CCW permit will allow you to carry a gun, but NOT a large knife. That's true in several other states as well.
I don't disagree with you on any of your principles. I just think that if you're really going to take them seriously, the kind of knife you'd be legally permitted to carry won't be sufficient to the task, and if you're going to carry something for that purpose in your gym bag, I can think of many things that would be preferable. The relevant rule here would be, to my mind, "carry the tool that's sufficient to the task." Or heck, find a better gym. You're seriously telling me that you go to a gym with no free weight equipment?
I have never personally been in a gym where there was NOT a myriad of better options for defending myself (including, incidentally, my hands and feet), that would be preferable to an untrained person with a pocket knife attempting to defend themselves against a gun wielding opponent. And, in many cases, such a person would be likely to get not only themselves killed, but also other people. I have no problem with putting up an armed defense. But if you live in a place where a gym shooting is a reasonable possibility, why not choose the right tool for the job?
Or if you carry a knife because you think that there might be a dreadful shoelace/bike injury, fine, that's your business. It's the self-defense folks who cause me problems, because they're the ones MOST likely to cause a ban on knife carry. Did you know that self-defense is NOT a legitimate affirmative defense for carrying a knife? That's a sad reflection on our times, but one that a responsible knife owner would do well to keep in mind if we want to continue to have the option of carrying a knife. If we're having such a tough time convincing fellow knife nuts that it's legitimate to carry a knife in a gym, imagine how a jury would feel.