Are you trying to meet the 10 years minimum to qualify for something, or getting more credits to get more?
The totalization agreement will let you use credits from one system to push you over the top to qualify for more than zero.
But if you're trying to build up credits in both programs, your approach works fine, it's what we do for my wife. She gets NI credits through child benefit (and at some point her self employment may be enough to pay some NI tax too), and we pay SS tax through self-employment. We could use a certificate of exemption to avoid the SS tax, but her earnings history in the US is small enough that she's well below the 90% bend point, so it's actually a very good return on investment for her to pay a small amount of SS tax to continue building up credits and earnings history.
She's older enough than me that this could let us have her take SS at 62 and me delay to 70, so that'd be about 12 years of her SS before I take mine and then she gets spousal benefit (likely a similar amount to her age 62 benefit). But those numbers get fuzzy fast, lots of assumptions and we're far enough off. To me, it's a small price to pay for optionality - but her SE taxes are truly small, a few hundred bucks a year. Might be different if it was thousands!