I had this but had also been the one claiming and the higher earner, and I paid it back (about £1,500 not £10k).
It is a shit system. In my case, when the measure just came into force I thought either a) DH was doing tax returns and had accounted for it when I was the lower earner or getting back into working again as he had done tax returns and asked me about CB or b) it had already been included in my tax which was all PAYE. There were a couple of years where I did a lot of short term contracts and my earnings went slightly over the threshold but were all PAYE. Apparently then I was also the higher earner but only just. HMRC actually told me I should stop doing tax returns, not mentioning anything about needing to if you claim CB and are a higher rate tax payer, while having all my salary details and CB details knowing clearly I did fall into that category. But apparently I should have for two years. They were nearly outside their own threshold to pursuing me, it took them so long to review it.
Then when I went to pay it on my account, good job I kept checking afterwards as there were a couple of extra messages where I owed another £150 and then another £30 or something with short deadlines to pay. But there was no alert anywhere about those messages so had I not checked I could have missed the deadline and been fined.
I really do not trust HMRC at all, and it gives me anxiety that they are still going to keep coming for me for something else I got wrong inadvertently, even though my tax affairs should be very simple indeed.
My mum's tax affairs should have been even more simple, someone on state pension with tiny private pensions and PAYE only. But they managed to mess hers up as well, always claiming she hadn't paid stuff when she had, and this was when she was in her 80s. Good job that she was on the ball, and that I had her back too.