It would make sense, we think, to be able to play a fast spell on my turn, let it resolve, and then have a chance to play burst spell(s) only before the turn ends

This breaks the entire game design. Every card in the set would have to be redesigned. The whole point of slower speed spells is that they are balanced by you having to pass the action to your opponent so they have an opportunity to respond. (In other words, LoR does not have a phase-based turn system; the currency is actions and Burst spells are balanced by being the only spells that do not consume your action.) Being able to cast a burst spell before passing the action to the opponent would let you do things like play Brood Awakening (summons three 2/1s) and then Iceborn Legacy afterward to give them all +1/+1 before your opponent gets the chance to respond with their Withering Wail, which would clear your board.