I think it’s fairly probably that she was the bigger earner in the relationship, so more likely to have put more into the deposit or the mortgage when they owned it together.
I’d lean towards it being more of a fresh start decision, unless the mortgage came up for renewal and the change in interest rates since they bought it made it tricky.
I know the rough area and the sort of house/rough market price to narrow down a Rightmove search and can’t see anything sold that looks like it… maybe I’m wrong, they continued to co-own for Arlo’s sake and actually Joe has bought her out…? I just don’t see his work paying enough to afford to buy somewhere, unless he has really taken off since I last saw him on socials…