There are many grappling styles, each generally has a different perspective on how to approach and handle the circumstances of grappling. The different perspectives led to different sporting rules. The different sporting rules led to further evolution and specialization in their respective areas. That specialization leads us to a point where it’s often debated that to be a “complete” grappler you need to train in all of judo, wrestling, BJJ, and Sambo (not to mention the various other folk wrestling styles).
It may be true that to compete in all four sports you need to train in all four sports. However, I don’t think it’s necessarily true that you need to cross-train at all to become “complete”. To me, a complete grappler is someone who can answer any situation. If you put them on their back they should either know how to fight from there or how to get to a different position. If they start standing they should know how to get them and their opponent to the ground in a way that doesn’t inherently sacrifice position. It doesn’t mean someone who can play De La Riva guard just as well as they can throw or can leg lock just as well as they can choke.
Judo as a martial art has all of the elements of grappling. Grip fighting, posture control, throws, guard passing, submissions from guard, guard sweeps, pins, transitions between top positions, submissions from the top. Judo as a sport de-emphasizes a lot of these, but they don’t stop existing in judo unless everyone completely stops practicing them. BJJ as an art has all of those same elements; again, as a sport we see certain deficient skills. American folkstyle wrestling, Freestyle wrestling, and Greco-Roman wrestling have many of the elements, but their extreme sportification has made it hard to find individuals who still know submissions and guard passing. Catch wrestling does still exist, even if the form of it you find is an anachronism recreated by mixing BJJ with folk wrestling. Sambo remains probably the most well-rounded, having lost the fewest number of skills to sporting rules, especially when you consider Combat Sambo.
From a purely theoretical standpoint, any individual who digs deep enough into their art could learn all the base skills. Anyone with the right resources could become complete, still only having learned the one art. From a practical standpoint, cross-training is pretty much necessary because of those sportifications. Many judo clubs train to the IJF rules rather than training in judo and just applying the techniques and skills to the competition when it arises. Few BJJ schools spend dedicated time working on throws for more than a class or two here and there. I have yet to find the high school that teaches Catch techniques as opposed to just sport wrestling. Still, it’s important to note that the underlying arts are not deficient as each just represents a different approach to all of the same circumstances. It’s the implementations that are deficient.