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I don't know when the Open variation had its heyday, but it was over by the 1960s. The Open is an OK alternative to the Closed lines, but to my knowledge no White players fear it particularly, though they might, like Reb, prefer to lighten their theory load.
Actually, the Open had its heyday when Korchnoi was playing it in World Championships in the 1970s. That's also when Karpov busted on it, so its heyday coincided precisely with its decline.
Note: Why does autocorrect automatically make "its" into "it's" even when it's grammatically incorrect? Gugh!
I personally like to play the center attack in the RL but if you wait until move 6 to play 6 d4 then you must be prepared to meet the Open so I started playing 5 d4 instead and I do it to avoid the Open ...
A great strategy: disappoint them before they disappoint you!