The significance of that number is Unown to me.
I suspect brainwashing Pokéballs are too far on the Grim Dark
side, if nothing else. (Though really, once that fact got out, we'd be seeing all-out war.)
Though yeah, training a Pokémon is a very involved process. Teaching your language is often needed, though some wild ones may have a grasp of the local human dialect already (say, the local Machop population likes listening to the early-morning exercise program on a scavenged radio). The Starter and other experienced team members assist this education, briefing a new catch on things like the Trainer's name, basic rules of behavior around humans, etc.
And teaching a new move almost certainly can take days of work, assuming the Pokémon is mature enough to handle it at all. I think the variations in level-up moves between games can be attributed to having different protagonists- different trainers will have different knowledge of moves, different skills in teaching them, and so forth.
Attaching Pokéballs on a team? I can see why that would be appealing... need to work out how that would operate, though. Two balls could probably synchronize their pocket universes to make the inner containers physically adjacent, but then there's still the actual walls to pass...