I've met anesthesiologists who do solely CCM. It's a little unusual but definitely not unheard of. This would be in both pp and academic settings. As far as the medicine goes, it comes back is what I've been told multiple times. Critical care is medicine, but internal medicine is definitely NOT critical care, if that makes sense.
As other posters have alluded to, don't choose a sub-specialty without realizing the implications of the specialty it's housed under. There are 3 (actually now 4) ways to get to CCM. Pedi isn't counted here because I'm assuming you don't want to do PICU. So, you're choosing between IM, Surgery, Anesthesiology, and now EM. So you need to analyze those specialties first and choose one you actually see yourself practicing in the event that something changes in the future and you no longer are able to do fellowship.
CCM is great and I love anesthesiology, too. To me, being in a pulmonary clinic dealing with COPDers was not appealing at all. Plus, I hear from my pulmonary colleagues that their fellowships tend to emphasize pulm way more than CCM. So IM was out for me and I definitely cannot ever see myself as a surgeon. EM wasn't an option for CCM when I was in medical school.
Anesthesiology was a no brainer for me, and I went into it knowing I'd apply for CCM.
A good question to ask on here of the CCM Anesthesiologists is if we had to choose one or the other (black or white, no in between or "it depends") which would it be. It's a little early for me since I'm just starting off as an Attending and have my first ICU week coming up, but as of the end of fellowship, I'd choose CCM.


I know, crazy right? Most general anesthesiologists think I'm weird that way, but I have a suspicion a lot of the CCM ones would choose along the same lines as I. Residency in the ICU is NOT a great look into the practice of CCM, at least not where I trained. Scut work abounds, and unfortunately that will jade a resident's experience and desire to actually pursue Critical Care.