This card is really, really cool. I think that the utility here might make this playable. As a creature its' a flash blocker, plus it has flying so you can end step this to fly over your opponent's monk tokens and kill Jace on your turn. It's much like a Vendillion Clique in this respect.
The Cycling ability is actually really good, BUT three mana is a tad expensive. On the plus side it's nearly uncounterable (unless your opponent is playing their own stifle effect), it;s a cantrip so you're not losing card advantage, and it can target a ton of different things.
As you mentioned Storm is a triggered ability, so this stops that. But you can also just hit fetchlands for value too. Sometimes stopping a planeswalker activation or ultimate is helpful too. Does this stop Modular from working too (I'm really asking)?
Stifle always suffered from a few unfortunate things. Stifle looks bad against Mental Misstep. Stifle is always a stifle and as such it's value is entirely relative to the targets your opponent is giving you. Also when you counter an ability with stifle and that ability is reusable you're trading a card in hand for basically nothing besides a short delay; this is bad in card advantage battles. This card replaces itself so if you're stopping something like a planeswalker for a turn you're still going to remain at the same card advantage count that you were before.
Oh and it pitches to Force of Will. And it fuels Treasure Cruise. I really like this card. The three mana cost seems like the only thing that could hold it back.