Well, they put quite a bit of their own money into refurbishing and decorating it didn't they? And it's probably an important place to their kids, since it's where they've spent a lot of time. Plus, it's where they go for Christmas and school holidays. Doesn't really make sense to give it up.
The Windsor move seems strategic to me for many reasons. One, it does allow them to choose a school close by all three kids can go to through age 13. So you're looking at nine years until Prince Louis is through.
Two, their new school has the flexible boarding option. I think they're not the type to send their young kids off to board full time, but this way, if the kids want, they could ease in- say, stay one night a week when they're younger and gradually increase if they want to.
Three, they are close to Kate's family, who are her trusted inner circle and who allow for some private and happy time for all.
Four, they're near the Queen, especially if her health takes a turn.
They seem to have been thoughtful in selecting a reasonably sized property that didn't need major renovations and paying rent for it.