You do realize that the purpose of hi, including bohi, is in no way related to tachikaze, right?

Any time someone talks about the "purpose" of something related to something as complex as Japanese swords lots of detail gets lost. Horimono of all sorts (of which bo-hi are technically a subset) were cut in for all sorts of purposes. Sometimes to conceal a nasty ware' (grain opening). I was looking at a marvelous antique with the freaking ugliest centipede carved into it. Obviously to hide a flaw. Other reasons for things like bo-hi in particular would be to change the weight distribution of the sword while minimizing loss of structural integrity (at least in the direction of a properly performed cut). Finally, some carve bo-hi and other horimono solely as an artistic expression. The best smiths will make the blade with the idea in mind that they will be cutting in bo-hi later and compensate accordingly. And a well done bo-hi is really amazing to look at. The hi on production swords are usually horribly wobbly and "soft" for lack of a better term. I was looking at a Yoshihara Yoshikazu daito recently that had the most precise, crisp bo-hi I'd ever seen. Amazing when you consider how they're cut in.

And for you trivia buffs, you can get a fairly decent tachikaze with most any sword, especially one with a high shinogi (yamato school shape would be the most obvious example of this). The tachikaze of bo-hi and high shinogi blades is related to turbulence forming in the "wake" of the sword during a cut. When you have proper alignment and can get enough proper tip speed you get the sound. I actually adjusted the shape of my favorite bokken to a very deeply angled shinogi-ji to create a very loud tachikaze with it.