I don't know what chemical or physical process renders a pipe "broken in" and I haven't seen any convincing explanation of what it actually means. But from experience I have found that it does indeed occur. I bought too many pipes too quickly and was an infrequent smoker so it took quite a while for the 20 or so pipes in my "rotation" to "break in". But I did find that the smoking experience -- taste and how much the bowl heats up in particular -- did indeed improve over time.
For example, a Castello shape 55 was not enjoyable to smoke at first, and another small artisan pocket pipe would get so hot I couldn't hold it no matter how slowly I sipped. After 10-15 smokes roughly, I found both had improved. Neither has a cake, but both do have a nice carbon layer in the bowl.
Just a complete guess, but wood, even dense wood like briar, is an organic material with pores that open and close and the wood expands as it heats up. Perhaps the imposition of a carbon coating, even if thin, conditions the wood so that you taste the tobacco, rather than resins or whatever else is in the wood.
If I had to do it over, I wouldn't buy more than 2 or 3 pipes at first, and would smoke the hell out of them for a while and see how they develop before buying any more.