I would say you have a kid who needs to get a life.
Honestly, I don't see this as being a realistic example or representative of what people mean by crosstraining.
If I can pare your example back a little, though, to say a grappling and a striking art and a more reasonable schedule I think there's something to discuss:
How about a kid who is on the wrestling team, training 4 nights per week in wrestling but only for 5 months out of the year. During wrestling season, he cross trains at a boxing gym 3 nights per week but mostly for cardio and technique, as his coach would kill him if he gets injured.
The other 7 months out of the year he trains Boxing 3 days per week, but amps up the sparring, even working in a smoker or two. He also adds Judo 3 days per week at the YMCA club, because the grappling is a different kind of cardio and he enjoys the takedowns.
Let's say the kid keeps going through college with this regime. I think that the learning curve keeps going for most people and that this kid would be consistently more capable than, say, a similar kid who trains in only one art.
At 1 year, 2 years, 5 years and 10 years, I would say that this kid has two major advantages over a single art practitioner. First, he will have the advantage of exposure to multiple arts and a diverse group of training partners and styles. Second, he will have the advantage of having learned how to learn. What I mean is, he will be able to pick up other styles and techniques faster because he's actually trained on how to train.