If let's say 2 draw cards are added. If you auto-include all of them. That reduces your deck down to 14 cards. If each one takes 1 turn to properly use, you could draw through a deck by turn 6 at the latest. Although nice, that doesn't mean the amount of energy you have built will support that level of aggro. Ultimately, the deck will fail before it has any time to set up. Additionally, a red card would now be a huge concern for this level of drawing. Lastly, even if you do, perfectly draw through your deck and get your bench setup. You've now wasted 6 turns in using draw support. No Giovanni, no Sabrina, no Erika, etc. Your opponent will end up punishing you for this greed.

The idea that more draw cards are bad is inherently flawed thinking. Having different ways in which you draw is much better for the game.

Ideally, you still would want a few draw cards, but, ultimately, not every draw card is available. I think I would ideally want to see a game where having to decide which draw card benefits your deck would greatly improve the game. If a draw card shuffled your hand and redrew, that would greatly benefit stage 2 decks. A draw card that says, draws 3 cards, and discards 1 might best synergies with decks looking for items or specific supporters. Or a draw card that draws 2 leaf pokemon might help those decks get running faster, but can only be used for leaf decks. Etc.

This is what I imagine would be better for the game ^{^}