Normally I'd say stay out of it/ encourage the young adult to make their own decisions. And ultimately, if she is absolutely dogged in this, then I would support her and hope for the best.
However, I have to agree that Kent would be a huge mistake. The uncertainty regarding the future of the university makes it a big risk and she could get a much higher quality and more reputable education elsewhere, as she is certainly qualified to do so.
Also, she has to have known that getting an offer at Edinburgh was also going to mean getting an offer at Kent - so if the distance mattered to her more than what the university has to offer (and she was always going to choose Kent in this circumstance) then why did she waste a choice by applying to Edinburgh at all? Does she also feel the same way about Durham and St Andrews?? It suggests she either hasn't thought about this much at all / doesn't understand the differences between the universities / is all over the place with her decisions.
As you will be financially supporting her I think she needs to show you the respect of carefully considering this decision. I'd also question whether she isn't prioritising academia / career prospects because she isn't that enthusiastic about astrophysics, and sees university as primarily a social experience. University is a great social experience but it's too expensive to be primarily about that. You are also not unreasonable to want to protect her, at 17, from making enormously expensive life altering mistakes (that you are helping to pay for!)
However, if she doesn't want to go really far from home, I would really listen to and respect that. It's a shame that she has wasted this year applying to universities she doesn't want to attend(!) but she also has the option of taking another year with grades in hand to apply for some different universities (with a bit more thoughtfulness).