the sparrows situation will be resolved in short order. cersei's trial is coming up in a matter of days, and so is margaery's walk of shame. hence the sudden decision (and not the smartest, i might add) by cersei/jaime to allow the tyrell army to basically take over king's landing, because there's no time to waste. my guess is cersei's trial by combat, with Zombie Mountain as her champion, will set the stage for that battle. the Mountain will kill whatever champion fights for the High Sparrow, then he'll crush the High Sparrow himself, and then the Tyrell army will kill the rest of the sparrows. after that, it's off to Dorne. it will take a lot longer than that for Starks to retake Winterfell. and Dany's been around for years now in Essos and nobody's been too bothered by it, no reason that will change any time soon, besides Dany has unfinished business to take care of in Slaver's Bay before setting off for Westeros.
and you give both cersei and jaime way too much credit. both have shown plenty of recklessness and short-term thinking over long-term strategy. kevan lannister basically wrested the high council from cersei for that very reason. after tywin's death, kevan was the only thing standing between cersei and a whole host of dumb decisions driven by her need for vengeance. and even then, she still managed to screw up by conspiring to aid the sparrows and use them against margaery, a plot which backfired spectacularly. it's been well-established that cersei is obsessively driven by her need to protect her children (again, ironically, usually in ways that backfire) and seek vengeance on her enemies, real or perceived. and jaime is basically driven by his need to please his sister, and she's so adept at manipulating him, even when his better sense tells him otherwise, he falls for her tricks. between that, and having his daughter die in his arms only moments after finally acknowledging him as her father, he's also driven by his passions rather than any kind of logic or long-term strategic planning.
we've got 3 seasons left including this season. even though this show has a tedious ability to keep delaying the inevitable (see: Dany's endless tour of Essos), the end is finally coming into sight. i expect the Sparrow issue to be resolved in the next 1-2 episodes (they don't make that tyrell alliance, only to wait til the end of the season for it to actually happen), and the 2nd half of the season will feature 1) Lannister army marching on Dorne, 2) Stark army forming in the north, with the battle with the Boltons sometime in the last couple episodes, well after the Lannister army is well on their way out of King's Landing, and 3) final episode ending with Dany finally setting sail across the sea. Next season will resolve a lot of these alliances, with Starks and Tyrell's allying against and finally defeating Lannisters and consolidating power, while Dany and her Dothraki/Unsullied/Merc army slog across Westeros trying to rally support to her claim, probably ending with Starks vs. Targaryen faceoff, before final season features Starks and Dany realizing the true threat from the North, and uniting to defeat the White Walker invasion which is what this entire series has always been leading up to, the clash of ice and fire.