For me it's the opposite, I used to do boxing and other ma, then I went into cma and now my training is a hybrid of a lot of things, but boxing has taken a key place because of the sheer value of the routines associated with developing the skills required.
cma may be complete, not in all formats, there's a lot of bits and pieces schools of patched together methods. May look complete because there is a lot, but in truth, the majority of any style of martial art is incomplete in the sense of the word regarding what you fill your toolbox with.
If someone wants to learn to fight competitively, I would recommend boxing over cma.
why?
With boxing you will have a reasonable amount of ability in boxing and defending yourself inside of 1 and1/2 years.
With tma, this is barring innate talent stretch out to sometime longer than 5 years.
Cma is a crap shoot in my experience. There is a lot of exciting things in it, but it is difficult to know if what you are getting and practicing has tangible value. especially when it gets wrapped in a lot of mysticism which can be a little too prevalent in a tma school whereas in the boxing gym, it's you vs you...and that other guy occasionally.
Much more in the moment type of reality that zen people like to talk about and sit with, but I've found don't personally have the stomach for when it comes right down to it. No offense to those who find themselves in the sh.it and practice zen.