Don't get me wrong, I love using category theory, and in the stuff I do it is absolutely fundamental. I am also a big fan of oo-categories and all that. But I would never do research in category theory.
The kind of category theory I've used (and that I've seen used around me) is always pretty basic. It's stuff that you could pretty much prove yourself, once you know the correct definitions. I've certainly never read a research paper in category theory.
I guess my point is that, in my experience, all the category theory that I've seen used was never invented by someone doing research in category theory. All the concepts were invented by, and all results proved by, people who needed a bit of category theory for their own work.
That's why I've always been a bit skeptical about category theory for its own sake. I guess that's the issue I take with it.
And, again, don't get me wrong. I would love if 'applied category theory' actually were useful to solve concrete problems. I would love if we could phrase statistics in categorical terms and got some mileage out of it. And it's great that people are trying. But I'm still a little skeptical.
Does that make sense? I hope it's clear from this comment that I'm only voicing my opinion, and not trying to start some kind of comment war.