There are all kinds of teapots made from all types of materials, so you're wondering, 'which is best to use'? or, 'what is the best kind to buy'?'
The quick and short answer is...the one you love. Some of us are drawn to one type or another, and some of us, like myself, love them all. I have pottery, china, glass and silver in my collection.
If your pot is glazed on the inside, you may be able to use it for different types of teas and tisanes, but some are not, and the oils of the teas will leave a residue.
Yixing, tetsubin and other similar pots will absorb oils creating a 'seasoning' and as the years go on, you will enjoy richer and more flavorful tea. You will actually dread having to 'break-in' a new pot. For this reason, if you are partial to one type of tea (especially a strong tea), it is advised to use one pot for that type.
Delicate teas like white tea, if brewing in a pot where you usually brew Assam or Earl Grey, will absorb those stronger flavors.
Check with the manufacturer or retailer when looking to buy to see if the different types are sealed or glazed so they won't absorb oils, or use one pot for one type of tea, or use a glass one. Glass will not absorb oils, and is dishwasher proof.
Why yes, they are! Tea vessels (they haven't always been short and squat like a pot) have been collected for ages! Ever since 'fashion' became noticeable at the dinner table instead of things just being utilitarian, it became a 'thing' to have a collection of tea sets for different occasions, formal and informal, and different seasons like Christmas and Springtime.