I will strongly disagree with you...
Actually he did promise but he lied deep inside.... You know, when a person lied to you, just get them drunk and they will say the most unexpected but real answers of what you are asking for... and Kaoru sadly said the total opposite of what he initially said and promised...
This is an inner battle between his selfishness, past experience with red string of fate and his own principles... It might be unnecessary to you but to Kaoru's character development.. this weak side of him should be opened and explored.
Hara is mad enough to only crave for him, how much Kaoru could return that one?? That is the most important thing that Kaoru could answer..
For me, inner battles are much important as external ones.. It defines you as a person and molds you as a person..
In the prequel (or in the earlier chapters?) when Arako cut his string, Kaoru told him that if the feelings are strong enough the string will reappear. He promise to cut the string but he knows better than anyone that cutting it might not change anything. He's hurting but he thinks there's nothing he can do, he saw people he went out with have their string attached in front of him and they all eventually left him. The same is just happening again.
But yeah, I think he should at least talk to Hara about it. Just waiting won't help.
But i totally understand why he is keeping secret. İf he says him now , he will want to cut it and trying to get rid connection with her. İf he don't tell he don't suspect rope to connect with her and when he realized he live her , he will say him they have already connected. So sad moment but ass person who left behind and see all persons living him he totally accept fate. Now he is only trying to buy more time with him. And showing big sacrifice keeping inside him
Soo unnecessary. He promise his partner to cut it. So what he's doing (●￣(ｴ)￣●)