It's like people keep forgetting Renka's the heir/sort of replacement head for a China-spanning martial arts alliance of people that predominately use what 'normal' people would consider bullshit martial arts. Thousands, tens of thousands, even hundreds of thousands of members is entirely possible when their roster is drawn from a country with more than a
billion inhabitants.
Can you think of no use for a literal army of martial artists for the Hyodo Clan and associated allies?
And as to 'but she's Kenichi's!' she's not - and never was even in canon. Oh sure, Renka chased Kenichi just like other girls did - but what did that end up
doing for her? She didn't get the guy she was interested in, she never returned home to manage the alliance she left to find it's original leader (her pops), and she basically got stuck working at a chinese cafe in fetish gear (seriously what else could you call her second outfit). The organization in which she takes pride was abandoned, she did not get her feelings reciprocated, and neither of those are really satisfying.
So 'getting' Renka is good for everyone.
- Renka gets someone who's not a whiney bitch about relationships and will not flee from her advances, who is themselves more prone to the kind of grandstanding bravery that Renka likes.
- Issei gets another 'would love to be involved in crazy quests because they're classic martial arts adventures writ supernatural' girl, and those are always helpful.
- Renka gets someone that's actually better than her in terms of how dangerous he is (hard not to be as a sun dragon god thing), and represents multiple ways to breathe new life into the alliance and make the fact she's still not returning with her dad, the original Head less of a problem.
- Issei gets access to a literal army of martial artists that could probably be introduced to basic magi-martial-arts-capable, and thus be both a massive force and a meaningful one.
- Kensei doesn't get hounded to return to a place he threw up his hands over and went 'I'm out' about, and ALSO doesn't have to watch his daughter further muck up the place he left in a futile attempt to drag him back.
- Kenichi doesn't get hounded with yet another, in his eyes, crazy violent girl when he's got Miu to hound after.
Pretty much every party involved 'wins' by the Issei/Renka angle - and that's why it's a good idea.
...That, and as Issei just blatantly drooled,
it's a real sexy chinese fighter girl, and that's all kinds of fetish fuel to an otaku-rooted hero.