Matija Sirk's answer is very good and it's true that learning different sorts of positions will improve your overall chess skill. If your goal is to be the best chess player you can possibly be, and if you are young and talented enough that that may be very good, then I say you should definitely play lots of different openings.
"Chess is a lake in which a mosquito can bathe and an elephant can drown" (Indian saying).
Suppose you are more like the mosquito?
Suppose that, in addition to chess, you have a job, a spouse, some kids, maybe even (gasp!) some other hobbies! Maybe you want a good portion of your total time playing chess to be actually playing chess, rather than studying?
In that case, you can play the London exclusively, forever.
Even at the highest level, it is only recently that players play all sorts of openings. Bobby Fischer had a relatively limited opening repertoire. Lev Alburt, who was a GM (if not quite at Fischer's level) played the Alekhine's defense as Black pretty much all the time.
I think that, unless you are going to try to make chess your career, your goal should be to get as much enjoyment as possible out of the game. If the London makes you happy, go for it.