Sure the PS4 leads this gen, but it didn't last gen and i think had Yakuza games been released on X360 the fanbase for this series would be bigger, especially here in the US. That's why i mean when i say that SEGA has limited the audience of Yakuza games by not going multiplatform. Hell, even the Wii U got an HD port of the first 2 games, no reason for the XBOX not to get a single title here.
There's several factors to consider;
1. The Playstation series of home consoles have been the dominating devices since the original release with the exception of last gen which now seems like an oddity rather than a general rule (Not that it'll last since consoles don't have much left in them I fear.) so it'd be more logical to support that platform than any other.
2. SEGA actually approached all three console manufacturer prior to the release of Yakuza and who would be willing to support the title. Only Sony showed any interest and this is why the series has been established solely for Sony's consoles from the get go.
3. Yakuza is made first for Japan and than everywhere else, now if the original Yakuza game made a sizable splash, it might have slowly shifted to a worldwide focus. As it is it hasn't. This returns to the bit you mentioned about Nintendo, Nintendo has a sizable stronghold in Japan, which is why SEGA attempted to broaden the franchise on the Wii U, it failed. What makes you think the Xbox would be any different?
It's best to remember the Xbox 360 in general saw lower sales for Japanese titles vs Western titles, now this could be because they were poorer than their Western counterpart, but it's not like the 360 itself showed it had a decent userbase of gamers who liked Japanese developed games. It's the reason why series like Star Ocean, Idolmaster, Tales Of... etc went back to the Playstation family of consoles after their failure of trying to break into the Western market via the Xbox brand.