You may have difficulty finding an academic ICU job if you don't have a CT fellowship, too. The reason being that many cardiac surgeons refuse to let their patients be cared for by non-dual-trained intensivists, unless you come from a CCM fellowship which is a lot about cardiac critical care (Columbia, Duke). Which automatically means that the fellow misses out on other stuff (e.g. MICU).
The CTICU being one of the big moneymakers for hospitals (because cardiac surgery is), CTICU coverage is incentivized and important for the anesthesiology departments. If you can't cover the CTICU, you may not get hired for a combined academic job (I've been refused multiple times by my own residency program, though they are always happy to offer me an anesthesia-only position).
There is also a 10-15 year-older generation who got to do combined CT-CCM fellowships in only 18 months, who you're competing with for academic ICU jobs.
Plus cardiac surgeons are among the biggest PITAs in the surgical ICU world. The ego seems to be inversely proportional to the knowledge (Dunning-Kruger). It usually helps to have the cardiac anesthesiology training to shut them the F up.
Hence my usual contention that doing a CCM fellowship after anesthesia (especially without cardiac) should be reserved only for the most passionate.