Ok, so what’s the background? Usually by time diagnosis has been made dementia has long since started. This is seen by personality changes, decline in executive functioning skills, suspicious thoughts, irritability . All those put a huge strain on marriage and relationships between people. In turn your stop mother may have been true going to make sense of a relationship that was changing for what appeared to be no reason- she may have been frustrated, irritated etc and generally the whole thing became a confused slightly toxic interaction. Please do not underestimate the impact mental illness has on the partner as well as the sufferer, almost all relationships break down under that pressure.
is it possible that your father wanting a divorce has arisen because he was beginning to suffer with dementia ? Do you know why and what and when led to the breakdown in relationship? Does your step mum want the divorce? Does she even understand the reasons, even if she doesn’t agree?
you are right that a reason is now no longer required by process, but if you have proof that the reason he wants to divorce have nothing to do with his mental decline or repercussions of that, and were pre existing problems before his decline started, and continue to this day, then I think you would have strong case to argue he still has a “right” to divorce even if he cant be deemed competent right now to make that decision from scratch. So if there were issue like your step mother committed adultery..then it becomes much more straightforward and even a slight safeguarding issue that he should be allowed to divorce as per his wishes.
if the wish to divorce came out of blue quite recently and no one really understands why, and he didn’t or couldn’t tell you why at time, then you will probably struggle more to legalise it.
maybe there is an option for a separation in that case…but clearly that leaves financial and next of kin issues in the air