There are at least 3 reasons I can think of to be proficient in unarmed combat if you carry a firearm: 1) While carrying you may be in self defense situations where you don't want to escalate to presenting your firearm, let alone deadly force. Knowing how to disable, even temporarily, an attacker gives you a chance to get away and gives you options. 2) You may not always have your firearm with you (places where it is prohibited to carry or you just don't happen to be carrying that day; 3) Weapons retention and ability to deal with an attacker who gets to close (and even the most alert person can't keep potential threats out of striking distance, particularly since a person can cover 20 ft of ground in about 2 seconds).
Any martial art or combat system (those are two distinct things) requires a lot of sweat, often some blood and an investment of significant time and money to become proficient to the point where it is likely to be ingrained in muscle memory and useful in a real fight.
I have a 2nd Dan black belt in moo do kwan Taek Kwan Do (rougly 9 years of regular study). TKD is fun, and even with 2-3 years of practice you will realize some benefit in self defense ability. Knowing how to throw a punch and kick, increased foot speed and flexibility, and sparring experience will be of some use. BUT, TKD is a sport before it is a practical self defense system in my opinon, even in ITF schools. Learning pumsaes (forms, same as katas in Karate), the concept of block followed by strike, the prohibition on any strikes to eyes, throat, groin, knee, etc. and rules of sparring make TKD an art that doesn't translate very well to a real workd street fight. I'd assume the same applies to karate and even BJJ as taught in the lower levels in most schools.
I've been studying krav maga for 2 years and IF you have a legit teacher and apply yourself, I think it is much, much more relevant to a street situation. A good school will teach you the basics of punching, kicking (including front kicks, side kicks, round house and back kicks, similar to TKD/Karate but modified to make them more practical) and blocking ("360 defense") AND teach you real world techniques applicable in myriad self defense situations. The big differences with krav are: 1) from they outset it teaches simultaneous defense and offense -- eg a block is always accompanied by a bursting, explosive punch, not followed by a punch, 2) the concept of "retzev" or flow -- in a real fight there are no breaks or pauses if you want to prevail, you must hit hard first and keep hitting until the threat is eliminated and 3) everything goes -- eyes, throat, knees, are all not just legitimate, but in fact preferred targets. It is pure self defense, not an art or a sport.
One big caveat -- there are a lot of BS krav schools out there. Krav is "hot" and a money maker and unscrupulous practitioners of other martial arts take advantage of that. I've seen TKD and karate schools suddenly start a krav program after getting a certificate following a weekend of training with some bullshido artist (eg, see the Krav Maga Association headed by "Professor" Marty Cale.) Do your research to find legit schools. Those schools don't advance people easily. KM is deceptively simple. The fundamental principles requrie a lot of practic and technique to employ reliably and effectively.
If you can't find a good KM school I'd say look for a good, old fashioned boxing gym.