On the topic of Lim-Dul's Vault: I do not reccommend adding it to your deck. There are a lot of reasons I can give if you ask me to, but the main issues I have with it are that on its own it doesn't make an immediate impact on the gamestate (ie more cards in hand, Storm's version of "board presence", I would say), for which it demands more resources.
As for Burning Wish, let me just say this. Having played the 16-cantrip build, my average gameplan has become something along the lines of cantrip/discard T1, cantrip+discard T2, win T3. This is simple because it requires only 2 colors (UB), and my mana base fully supports those two colors. At any time I can count on my deck to reliably produce lands giving me the mana I need for my early game work, allowing me to save my Petals for PiF or for post-Ad Nauseam action. Including Burning wish as a key card means that suddenly your deck depends on three colors to reliably produce you a win on an average of Turn 3. This requires you to either crack your petals early for Wish, or for you to use lands like your Badlands which will not allow you to fulfill all of the functions of your deck. Pre-combo turn, running a 2cmc prep spell cuts down on your actions-per-turn, making it much more difficult to dig+discard T2, say. During the combo turn, BW is nice as long as you can pay for it, but we're not worried about combo turn, we're worried about getting there. Also, this may be a non-issue, but if you're concerned about discard against you, Preordain is better in that sense than Wish because it puts things on top of your deck, safe and sound, instead of right smack in your hand for everyone to know it's there.
tl;dr, other decks, like TES, are faster than we are, but we are still competitive because we have an advantage of our own: disruption. We can't play all the same cards that they do, because we have a different gameplan. Balancing between dig and disruption pre-combo is something that makes us special.
If speed above all else is your objective, don't hesitate to consider other, faster combo decks.

