BJJ isn't perfect. If you're fighting an unskilled person and use BJJ, odds are heavily in your favor to not just win, but hurt them pretty bad.
If you fight a skilled striker (boxer, muay thai etc) and manage to get them to the ground, it's game over for them, unless they are capable of getting back on their feet and/or have good defense against BJJ. Often times, if they don't have good take-down defense and/or any BJJ/wrestling acumen, their pretty much a fish out of water.
If you fight a skilled olympic-style wrestler, you will have met your kryptonite, unless you've trained to handle wrestlers. While they might not beat you on the ground (unless they slam you on your head), they will certainly neutralize your threat and know how to get back up easily. Wrestlers won't submit me, but their exhausting to roll with. They just know how to manipulate their bodies and yours in such a way that makes BJJ feel more like a task than an art. You sometimes go fully on defense mode and find it futile.
I've always felt that the best combination to have are solid Muay Thai + BJJ + Wrestling skills. I am not too sure that the idea of getting a black belt in one and then slowly trying to become proficient in the others is necessarily the best approach either. I think a well balanced approach, with equal time dedicated to each will make you a more complete fighter/MMA practitioner. I believe that if someone is serious about their training and devotes at least 3 years of weekly training (3-4x/week) to these three disciplines or just trains at an MMA academy that integrates all 3, you can be good enough to handle yourself well against the vast majority of people and fighters that are not pro-level. I also believe that if you are well versed in all 3 of those, you can/will most likely take out an individual that has one-dimensional experience in just one of the arts.
Also, you can easily interchange muay thai for boxing, but as someone that trained in boxing for years, I would have loved to have truly developed leg strikes and the use of knees and elbows from an early age. As you get older, it won't be an opponents skull that hurts your elbow, but instead it will be a less obvious opponent, like arthritis.
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