After sufficient rumination, I am prepared to share my experience.
I only have maybe 15 to 20 briars, and maybe 10 or so cobs. I do believe in resting the pipe for a day or two between smokes, and when I first started, I did not have enough pipes to rotate. Bit by bit, I added more pipes. Once I got to around 15 or 20 briars, I no longer felt my enjoyment was hampered by a lack of pipes, and I have not bought another pipe since.
None of this has been intentional, and I do plan to buy more pipes. I just haven't gotten to it yet. The last time I bought a pipe was 2018. What I would really love is to have a limited collection of very nice pipes and to toss out most of my knockaround basket pipes that I still smoke.