I don't think it is the most important thing. BJJ is more permissive than wrestling or Judo, allowing most techniques from those sports and adding more. With such a glut of allowable moves, it is easy to go down a rabbit hole of learning hundreds of techniques and being hardly good at any of them - the fancy mess Bruce warned about.
For mma or self defense, there are abilities that I think are indispensable - hiding behind the jab, defensive wrestling, escaping bottom positions, closed guard and standing up technically, break falling, defending power shots such as the overhand right and possessing knock out power with clean striking technique that you can threaten with anytime someone over commits to an attack, which will force them to act right.
There isn't a whole lot of a point in learning other stuff before you get that stuff for mma training, because it gives you the base for further learning and exploration without losing as much IQ. Then you can start focusing on a game plan unique to yourself or your school - pulling guard, scoring takedowns and finishing with submissions or ground and pound, or remaining up and winning with superior striking. Which ever of those three paths you pick will have indispensable techniques as well, but you don't need all of them. You probably want some capacity in all of them in the long run.
Without knowing as much about different grappling rule sets, I imagine you could come up with a similar list of indispensable abilities. I think it is natural to think wrestling is indispensable for no gi, and if you see yourself being a submission grappling fighter in MMA or being able to throw / pin / arrest someone in law enforcement then I think it might be, but if you are only worried about the sport of submission wrestling, I don't think you can say stand up fighting is that important, because you can win just fine without it.
BJJ schools don't have weaker take downs than Judo and Wrestling because they are weak people. They have weaker take downs because they don't have a sense of urgency to learn them because they are dangerous and they can get by without them. Also, many fine BJJ schools have Muay Thai kick boxing, and from a self defense perspective, their students will defend themselves first from standing with that and then resort to BJJ if forced, which is a classic way of thinking about it.