Why do we give reverence to the possessions of a tzadik if one of Hizkiyahu’s praiseworthy actions was destroying the staff with an iron snake that Moshe made?
In contrast to to some hassidic sects, with which you are apparently familiar (e.g. Chabad), mainstream Judaism doesn't "give reverence to the possessions of a tzaddik". A tzaddik's home in hassidut, as by some roshei yeshiva, sometimes has the halacha of a yeshiva/beit midrash because Torah lessons are given or studied there, but that's regarding the room of the classes and study, not the bedrooms, bathrooms, walls, floor, or address number. If you have a study in your home, that also deserves a certain amount of reverence. Nevertheless, the question is, if Moshe made the brass snake, it must have been fine, so why did Chizkiya do away with it? The Tosefta (Av.Z. 3, 19) explains that there were people in his generation who mistakenly thought idolatrous thoughts regarding that object, so it was counter-productive.