HOUSTON — Gerrit Cole grew up loving the Yankees, has excelled in the postseason and, with the caveat that neither Pittsburgh nor Southeast Texas reside on the Acela line, appears to handle media crushes adequately.

But what if the impending free agent Cole, once his Astros win their second title in three years, simply wants to go home to Southern California and accept Angels owner Arte Moreno’s gigantic check or — even worse for the Yankees — the Astros use their championship revenues to retain him?

Do the Yankees then capitalize on this starting pitcher-rich free-agent market by going aggressively after high-end arms who might not be as strong a fit in their unique environment?

Such is the pickle in which Hal Steinbrenner and Brian Cashman have put themselves: With a nucleus good enough and mature enough to win the whole thing, the Yankees absolutely must upgrade their rotation to keep up with — and surpass — their fellow industry powers. Yet somewhere in the dark recesses of their organizational minds, they should worry whether they’ve already blown their best opportunities.

Behind Cole in this class you’ll find, in alphabetical order (we’ll officially rank them shortly), Madison Bumgarner, Dallas Keuchel, Jake Odorizzi, Hyun-Jin Ryu, Stephen Strasburg (assuming he opts out of his contract with the Nationals) and Zack Wheeler. The best guesses state that Strasburg would top his pref list with the Nationals and maybe the Padres, given his San Diego roots, and that Bumgarner would prioritize the Giants and the Braves, who play closest to his North Carolina home. Keuchel, while an asset, looks more like a mid-rotation guy than anything approaching an ace nowadays, and Odorizzi looks like a notch above Keuchel. Odorizzi found something. Ryu, who very much pitched like an ace in 2019, lacks proven durability and will enter his age-33 season in 2020.

Wheeler, entering his age-30 campaign, offers clear intrigue. He survived the Mets jungle and ultimately excelled in it, and he enjoyed New York just fine. With a more stable culture and more sophisticated analytics, could the right-hander take his great stuff to the next level as a Yankee? Or would the Georgia native just as soon go home to the Braves if the dollars are there?

Now, to be fair, it’s not like guys like Cole, Patrick Corbin, Chris Sale and Justin Verlander were all slam dunks at the time of their respective availabilities as major leaguers. Max Scherzer was, except he shopped his services in 2014, Year 1 A.E. (After Ellsbury), and the Yankees found themselves on an austerity kick. Nevertheless, the Astros used their magic to unlock further greatness in Cole and Verlander, who would have gladly waived his no-trade clause to approve a deal from the Tigers to the Bronx in 2017. The lifelong Yankees fan Corbin will start World Series Game 3 for the Nationals in the wake of a great first year in Washington, and the no-nonsense Sale ignored Boston’s bells and whistles and earned a ring with the Red Sox last year.

The Yankees passed on Sale and Verlander for timing reasons — Cashman didn’t consider them close enough to the finish line to give big pieces to the White Sox for Sale and Steinbrenner feared surpassing the 2018 luxury-tax threshold with a Verlander import — and they didn’t deem Cole and Corbin worthy of the asks posed by the Pirates in trade talks for Cole and by Corbin’s agent John Courtright.

Notice how well all of these high-risk pitching acquisitions worked out? Even David Price, for all of the agita surrounding his rocky, $217 million marriage with the Red Sox, helped them get a ring last year, softening the blow and creating some eternal goodwill.

You’d be right to say the Yankees offense ultimately hurt them the most in their heartbreaking American League Championship Series loss. You try to strengthen all units, though, right? The Yankees know that bullpenning ranks as a great next-to-last option (superior to going with a mediocre starter), not the best one.

“Starters are still the way to go,” Zack Britton said late Saturday in the Minute Maid Park visitors’ clubhouse.

The Yankees must go there now, somehow, and hope they don’t wind up yearning for their roads not taken.