[taylodl]

Yes, but she never bothered to offer any other alternative and also never addressed the gorilla in the room: conducting experiments in fundamental physics is expensive. How are we supposed to best use our limited funds?

You can't run experiments willy-nilly in the hopes that something interesting happens. We run experiments to test theories and the only tool we have for developing theories is mathematics - and we're ignoring when our mathematical models lead to nonsense such as singularities.