I think the advantage would be that they would be allowed to appear together in public again. Right now as we see, at the wedding for example, Sarah had to sit apart from her family. Eventually Eugenie and Jack will have children and Sarah's grandchildren will be royal, but she still won't be allowed to sit with them or appear with them at royal functions...even though she lives with Andrew. I would think that would be a very awkward situation that remarriage could help them avoid.
There won't be another large BRF royal wedding until George marries. She'll be at her daughter's wedding. When it comes time for James and Louise, it won't be televised, so they can do whatever they want. The only thing would be Christmas. But Andrew and the girls jet off to Switzerland pretty soon after the Queen's speech anyways. And once the Queen passes, who knows which way Andrew and the girls will choose to spend Christmas. And I don't know if Eugenie's children would be attending many royal functions.