But I'm not talking about move-sets. Clearly a Kakuna cannot learn the moves that make Beedrill what Beedrill is. It doesn't have arms. I'm talking about the stats. There's no reason I can think of for a Kakuna to not have equal base stats to a Beedrill, it just simply can't really do anything with them.
In the ideal Pocket Monster universe,
every pocket monster, evolved or not, should have potential to be used competitively. It should be all about the training, not superficial factors like stats. This should apply to every monster(Except Dunsparce and Magikarp, of course. =P).
I really like your idea. Right now, my favorite Pokemon are all fully evolved. In order, it goes Starmie, Nidoking, Milotic, Staraptor, Torterra, Lapras, etc. However, I
know that if there was an item like this, I would like a lot more unevolved Pokemon the same, if not more, than their evolutions. As always, there would have to be certain kinks to work out, for instance, imo it doesn't make sense for Magikarp to have Gyarados stats, because they're not the same at all, but for almost every other Pokemon, I see no reason not to have your idea into effect.
How would the Light Ball work if you used the item on Pikachu? Would it double Pikachu's Atk and SpA or Raichu's? Or would it not work at all?
EDIT: Speaking of which... Eviolite.
I feel like Eviolite was Game Freak's initial attempt at something similar to Evan's idea. Not the idea of making unevolved Pokemon able to be used on competitive teams, but the idea of boosting their strength and to try to make them somewhat on par with evolved Pokemon.
Something somewhat similar that I would like to see is a change in how attacks work. I think that as Pokemon use a move more and more, they should get better at using it. For instance, in the Anime, Ash has a Swellow that takes an entire episode to learn how to use Aerial Ace. At the beginning of the episode, it couldn't pull it off, but it could by the end. (I think this is right, might be a different Pokemon). I think that moves should also have a leveling system, and every 20 times or so that you use a move, the move gains a level, which boosts the power, accuracy, or like PP of it. Of course, there would be a cap (like lv. 20 or so), but it would make people think harder about deleting a move for a slightly stronger one if they've leveled up their first move some.
Maybe even have like varying cap levels, with the stronger ones having lower caps, so the weaker moves have more room to grow.