Its not a girlfriend that will stop Aqua here... Aqua and Ruby are in such a different wavelength that Akane and Kana can never reach....
I don’t see Akane as intending to have Kana as Aqua’s girlfriend (lover). She only need Kana to be Aqua’s girlfriend (chain) to limit his actions.
And it’s not like the dismissive opinion about “love will cure him”, she’s not trying to fix him, being broken is like getting high on drug for him, he’s addicted and not going to let it go. I think Akane had mostly given up on trying to fix him and instead compromise with just stopping him from killing himself. Aqua can go to the therapist on his own when he’s in the mood, fixing him is no longer her business.
Instead, Akane need to put Kana in position where Kana is even more likely to get involved if Aqua try something funny, and hope Aqua hates getting Kana involved more than he hates seeing daddy alive. Akane can’t take that role because even since before she’s Aqua’s girlfriend, she already knows. Aqua doesn’t need to hide everything from her and don’t have to be cautious about being caught by her. Kana doesn’t come with that luxury.
Guys Aqua loves to feel they are in control and making logical choice based on reasons (makes them feel like adult, mature and in control of their life). So he will choose the “best” option with minimal loss even if it’s not what he “wants”.
Assuming Aqua’s revenge has a golden hour, if Kana as obstacle can held him back long enough until the timing passed, Aqua’s more logical part will work to hold himself back with excuse like how there’s a high probability for failure, and he will need to go back to the drawing board, practically means he won’t do anything for a while.