Earlier quoted context omitted.
Anyone can replace a showerhead in 5 minutes. The only reasons someone would complain about showering with a crappy showerhead is either because they're staying in a hotel (although most hotels don't even tolerate that shit), or because they're a complainer. Just don't be the dweeb who uses teflon tape.
What's wrong with Teflon tape? It stops minor dripping if you have older pipes with worn threads.
Showerheads are generally NPS (National Pipe Straight) which seals with a rubber washer. So if there is leaking, the real problem is that rubber washer is missing or old, or the female piece is cracked. Adding tape often encourages cracking the showerhead female, as it pushes out on the threads and showerheads are often chromed plastic. This goes doubly when the pipe coming out of the wall is actually NPT, and the tape encourages you to really over tighten it. Tape can be useful sometimes to hackily make things better, it's just not a good default.