The simple fact is that despite while some instructors may try and tell you, no art can cover everything. Striking arts typically lack the expertise of grappling and weapon arts. Grappling arts usually lack striking instructions and weapons. And weapon arts typically lack empty hand striking and ground grappling. Now can arts incorporate some of these other elements? Certainly. However, that does not mean what is included is complete or even their area of expertise. For example, Karate's grappling techniques are essentially limited to standing grappling techniques (joint locks and throws), but lacks the ground grappling (note: I know a few instructors who would argue otherwise) aspects of Brazilian Jiu-Jitsu or wrestling. And then there is the aspect of not including any weapon arts; hence the term "empty hand." Even the popular sport MMA, which literally means Mixed Martial Arts, excels in striking and grappling techniques, but lacks any sort of practical weapons instruction and defense - because it does not fit into what what the arts wants to focus on.
Cross training lets you fill in those gaps in your training with instruction from those who make those gaps their area of expertise.
And cross training in other arts is not a new concept either. If you look at many famous martial artists, you will often find some form of cross training in their history at some point. Just off the top of my head, Fumio Demura, who allegedly opened the first dojo in the United States, started training in Kobudo (weapon arts) after receiving his Dan rank in Shito-Ryu. Shoshin Nagamine, founder of Matsubayahsi-Ryu, cross trained in Judo and Kendo for a time. Wally Jay, found of Small Circle Jiu-Jitsu, studied Jujutsu, Judo, and Boxing all prior to creating his own style. Even the most famous martial artist of all time, Bruce Lee, started his training in Wing Chun before creating his own system/philosophy, Jet Kun Do, but also trained in other arts such as boxing and Kali.
In closing, as someone who has cross trained in the past, and would like to again in the future, if you have the time and ability to cross train in another art that compliments your current style, do it.