It's a fair point. Gina Miller wasn't elected, but I don't see that it matters. The government must obey the law, so if that's challenged, it has to be a third party who takes the government to court. It could have been an elected MP, but that would possibly have meant taking one's own Parliamentary party to court.
Anybody can challenge somebody for breaking the law. Money usually puts people off.
The point about Miller having rich backers is a bit rich considering how many super-wealthy backers the Conservative and Brexit Parties have. I can't imagine they're donating money because they're all altruistic.