CBT gets quite a lot of props. It legitimately deserves many of them but probably gets more than it should, especially relative to "black magic" psychotherapies.
The main reason CBT is so popular in the industry is that it was designed from the ground up to be testable. CBT practitioners and CBT-friendly researchers have run a lot of tests, and they have found that CBT is effective.
For a long time, other modalities either weren't tested in this way or were only tested under CBT-friendly conditions. And this is a real black mark against them. But since CBT started eating their lunch from 2001 or so, other schools that could afford to started doing their own tests.
Guess what happened when psychoanalysts started running their own tests? If you guessed that they went home crying and gave everything up for CBT, you would be wrong. Instead, psychoanalytic-friendly researchers have found (empiricially!) that psychoanalytic treatments are effective, except for schizophrenia, just like CBT-friendly researchers found that CBT was effective for everything including schizophrenia (which really should have been a tipoff that something was amiss in the first place TBQFH). In other words, which therapy gets found to be effective depends a lot on which therapy the researcher wants to be found effective.
There are a ton of problems in measuring psychotherapy. Researcher bias is an obvious one. Ensuring that the things you're measuring are actually the things that you're supposed to be measuring (e.g. that the CBT patients are all actually getting by-the-book CBT, psychodynamic are getting psychodynamic, control are getting...what?) is another huge problem.
Across thousands of studies, the biggest variable in effectiveness of psychotherapy seems to be the therapist him- or herself. Some are drastically noticeably effective across a large number of patients and most are not. The effects of treatment modality, assuming you can pin it down at all, are seldom very significant, especially when blinds and control are used.
Other reasons CBT tends to be favored: emphasis on short duration is insurance friendly. Also, the 'cognitive' adjective implies that it has something to do with recent advances in neuroscience, which it doesn't.
(FWIW I've had both CBT and analysis, benefited from both in different ways.)