I think there are plenty of older golf courses in the US with little or no fairway irrigation. Hillandale, in Durham, NC, just a few blocks from my house, has been there since 1916 with no fairway irrigation still today.
What happens is exactly what others have alluded to; lots of native grasses, including a lot of common bermuda, that become brown in the summer heat and drought, but manage just fine. What there is NOT are uniform perfect lies in the fairways, EVER, any time of year, and that's probably the issue more than fears that there will be bare ground.
A number of years ago, after watching my lawn burn up in yet another blazing southern August, a friend and I were talking about that problem. I made the statement, "When we were kids, we never seeded, fertilized, aerated, nothing, and we had green lawns all year. What happened?"
His answer was, "We had clover and crabgrass; now you buy grass seed that is certified NOT to have "impurities" like clover."
And so it is with golf courses; the problem is not the absence of irrigation; rather it's the desire for perfect green uniformity and a great lie for your ball. That's not a rant, or a good old days lament, or anything of the sort. It's just what's happened, not only to golf courses, but to our lawns.
(And BTW, if you drive by my home, you'll see a yard where the homeowner will NEVER again throw grass seed, or fertilizer, or aerate, or even rake leaves. We've planted a bunch of native shrubs for the honey bees, and the rest of it is whatever Mother Nature decides should be there. I gave away my self-propelled Honda mower, and I use a me-propelled reel mower for the tiny patch of grass that's managing just fine on it's own, and I have a weedeater for when things get a bit unruly. But that's all.)