There is a fair overlap between the analytic-philosophy community and physicists and mathematicians. So the analytic community generally doesn't talk out of its arse about these things.

I'm from the other side of philosophy, the continental-philosophy area, which mostly talks about ethics and art and identity, so for me to talk about CTCs I would be talking out my arse.

Philosophy is, generally, very hard to read. So much so that reading Descartes' Meditations (considered an alright starting text) in my first philosophy course took me about 30 mins per page.

But, it seems to me that this is one of those areas where analytic philosophy seems to be breaching an area where actual experiments can be proposed and tested in a physical sense, and it leads me to think, what's the point? The logical (philosophical) consistency of light being a particle and a wave doesn't come in to the reality of it. Was it worth ancient Greeks wondering whether all matter was made of water?

I think similar questions can be asked about continental philosophy. I certainly read a lot of it as a lot of wank that could be answered by real-world surveys (what makes people happy? I dunno, how about we ask them). But I think questions like, how do we determine whether happiness is the thing we should optimize for in life, are still relevant, and philosophical, and more basic! I think the underlying basic question of CTCs might be, does something being a logical paradox actually prevent it from happening?

And, if CTCs are a physical phenomena that we can't observe (maybe, yet), what's the point of a philosopher wondering about them? Shouldn't that be a theoretical physicists job?