Part of the problem with DS is that there are known engineering solutions without good theoretical explanation, that is, we just brute forced some basic engineering solutions and keep hacking at them to get more performance, but don't have a good theoretical model of why those things do what they do. (Or have a theoretical model too complex to compute useful insight, which is another kind of problem.)

I think that this kind of approach is going to get us pretty far -- see how far we got on building bridges with no more sophisticated insight in to gravity than "things fall down; some things are heavy" or material science than "some things hard and not bend" -- but I think that ultimately, our longer term goals like AGI will require that we build theoretical models capable of explaining our current engineering progress and predict a new, deeper valley of progress to move to.

Of course, that's a lot like saying making progress on physics paradigms requires explaining high temperature superconductors (or other currently open problems). It's actually pretty normal for a field to be a mix of engineers being ahead and theorists being ahead.

Mathematical rigor is really a sign that you're in established territory and explorers have moved on, and much of data science is still under heavy exploration.