Thank you for the thoughtful questions and the thoughtful answers.
My answers: no, no, no (almost all of the time).
My answers are based on greene's logic: what if everybody helped themselves to a piece?
To elaborate on the last answer, I am responsible for taking care of a bunch of plants in our local park, which is technically also a botanical garden. And yes people do come in and take plants or cuttings all the time. I find it incredibly irritating. Instead of taking the time to ask (in which case they would be provided with an armful of free plants from the greenhouse and instructions on their propagation) people just assume that because a plant is in a public space, they can take it home.
I would have no problem with people taking a cutting from a plant with a zillion heads or branches, such that taking one or two would make absolutely no difference in its overall appearance. Or a plant that desperately needs pruning and is overgrowing in every direction, being trodden upon by passers by. In that case they might even be doing a favor. But people are not generally interested in taking cuttings from those plants. They go after the uncommon or slow plants and don't leave much behind.
I have learned to tolerate the fact that my years of work and planning can slip into someone's pocket every so often, and such is the price of working with public landscaping. Like a sort of tax. I have also learned to avoid placing desirable plants right by the entrance or in an area where people will feel free to snag a piece. There is a sort of art to camouflaging desirable plants with more common ones, so they do not stand out. Some plants I would not even consider putting in there, knowing they would disappear the next week.
Based on that experience I would ask that folks take a moment to think about the effort that went into putting plants into a public space for the public good, and the generosity often involved in community projects like parks and bot gardens. Is it really a good idea to take something without asking (which is often minimal effort)? Are you taking from your neighbors, essentially? Would it be all that difficult to source and pay for a plant instead? I'm not trying to be dogmatic here, just sharing my experience, and the related issues, and hoping there may be some community benefit from it.