@Enzed, you raise some interesting points in your most recent post.
Lugging around just-in-cass stuff, is generally seen as a bad thing in packing discussions.
So true. That is why poles should be in one's hands being used, and not in one's pack as dead weight. There is no point taking poles if they aren't going to be used while you are walking. More, if they are going to help you should you stumble or have some other emergency, they are of absolutely no use if they aren't in your hands.
I know people who leave them strapped to their pack. I don't understand that at all. I use mine everywhere, including towns and cities.
Yes, they can be helpful on inclines like the ponte lima hill.
Of course, and they can be helpful everywhere else as well. The physics of pole use doesn't change with the slope. People use them to increase their speed, reduce the weight on their lower joints, or some combination of both. If you don't want those advantages, and feel that your hips, knees and ankles will survive without using poles, that's fine too. They aren't essential, but they are always useful.
My hands like the freedom to be open handed, it's easier to take out my phone out of my cross body bag to take photos with my hands free,
If this is happening to you, I would suggest that you are not wearing the strap correctly, because if you were, the poles would fall away from your hands as soon as you released the handles. You could retrieve an handkerchief, pick your nose, take a photo or any of the many other things one might contemplate because your hands are free of the poles.
In contrast, if you are carrying a simple wooden pole, at least one hand is never free of the pole, unless you put it on the ground or rest it against some convenient object, which you would need to do if you needed to use both hands to retrieve something along the way.
A simple test of whether you have the strap the correct way around on your wrist is to hold the poles in front of you and let them go. If the strap sits between your thumb and fingers, it is the wrong way around. If the handle falls away from you hand, and the strap is just around your wrist, then you are wearing the strap correctly.
And the click click noise can be distracting from the sounds along the path like bird song and wind rustling the leaves.
I am a little puzzled by what you mean here. If you are talking about the tapping noise of your own poles, you are entirely in control of that. Make sure your 'rubber' pole tips have not worn through so the metal tip has been exposed, and carry some spare rubber tips. If you are talking about other people with poles tapping away, I suggest you have no control over that at all, and it isn't a good reason for you not to carry poles. In either case, I don't see this as a valid reason not to carry poles.