My beautiful Iwachu tetsubin (teapot versions) that I purchased as a rookie have had to adapt to other purposes or they would never be used.
One is a magnet holder (seriously. I need a tiny, somewhat powerful magnet to get sample tins out of washi tins

) which it does admirably!!! I never lose the magnet!
One is a paperweight. Again, well done.
And one does get rare use for homemade grain teas.
I say this seriously, not sarcastically. It seems just about everyopne who paid tuition for tetsubin "teapots" does not use them for tea.
Teavana's army of propagandistas wrote:... the best teapot for brewing tea ...
... is far from true, IMHO, for reasons already given by Poohblah. Also they inevitably seem to grow larger as our needs for volume shrinks.
Having said all that, Adagio has several below your price ceiling ... though they are a tad larger.