It might be financial, but there are far more reasons for this than financial and that you can't see other reasons doesn't mean it doesn't exist. We can't know what they would do if the financial situation was different. People are complicated and there may be multiple factors involved. Even with the kids in school full time, with additional needs, there are a lot of potential factors to consider as well as the needs/wants/preferences of the adults.
My parents lived separately a lot when I was a kid. This was explained as a mix of my father's job involving a lot of traveling and my mother benefitting from living near her family. Sometimes this was only during the week and we'd be together on weekends, sometimes this was for months at a time. My mother didn't work for most of this (no benefits, wasn't in the UK).
When my father remarried, he lived separate from his new wife until I finished secondary school. The reasons given was their plan was to sell my father's house, move into her address and my father was concerned about my brother and I having access to our mother (he had full custody, she wanted nothing to do with us, he wanted us to have the option to try if she changed her mind), my brother and I have disabilities and they were in conflict with our needs and the new wife and their plan alongside not wanting to disrupt my education again. This was considered good parenting, not some scam.
I can't say he would have done things differently if his finances were different, I can say that if he hadn't been pressured to remarry after he got full custody (warped ideas from his family that we needed a mother figure), he probably wouldn't have. He's been merrily living alone for many years now, and I think (as I thought before he remarried) he is happier and more himself that way, he was just unfortunately in a cultural space where doing that with kids or when in a relationship was seen as unacceptable. With us all grown up, fewer people care. It may not seem normal or acceptable for them to live separately, that doesn't mean it's automatically wrong for them or that they're doing it for bad reasons.