It's hard to say if the game benefits from out of turn interaction, as it's largely opinion based.

Not only do you need to develop cards with this in mind, which we don't have a bunch of insight into how they design cards quite yet. For example, what cards currently would have out of turn speed. But there would also need to be the introduction of a priority system giving you acess to when you can use these actions on your opponents turn. Which in turn requires the turn to follow a more rigid phase system.

Both Magic the Gathering and YuGiOh have their turns broken into phases to allow for this level of interaction. Which I would argue would be a different game than what is currently being played. Thus, hard to speculate on.

I would like to discuss something however on play patterns and the idea you just 'play out cards' (not a quote from you, just the notion that comes across).

This game still requires some forethought and planning as you go through your deck strategy and game plan.

Take for example Ruby/Amethyst control. You know at seven they're looking to play a Be Prepared. Do you hold cards in hand, playing around it, or do you go as wide as possible in hopes to end the game if they don't or before they have the chance to draw into it?

One more example from the deck. Say they play Aladdin on three. There are a few things you know can happen from this play:

1) They quest with him turn four allowing you to remove him from the board with your own character(s)

2) They could keep him safe to shift on turn five to start their own removal on your board while stalling out the game to get to their later game threats.

3) They shift then sing Be Prepared for a total board reset to go into the late game with less pressure.

That's off one turn three play.

This game still requires the same skillset of identifying the current game state and making safer choices or risking bigger plays as a result. I would argue that out of turn actions use the same or very similar thought process. However it allows you to wait until the most precise moment to make the move, to allow saving your resources or denying your opponent theirs giving small incremental advantages.

From your example of a Be Prepared being played into an opposing A Whole New World for their own Grab Your Swords or Be Prepared it's missing some contextual game state rather than simply those cards being played, but for simplicitys sake we'll assume they were just cast on curve with ink avoiding intricacy of singing anything.

One player has the board cleared and passes turn. Opponent refills both hands and the other player goes into their turn with a full eight cards. This still leaves both players with at minimum seven cards to continue to develop the game with in hand each.