Severely shaved banks (as we have today) evolved. Mower heights during the Golden Age is just one tipoff. That doesn’t mean architects didn’t have roll offs toward water. It just means the ball didn’t roll nearly as far as it does today.
Do you know an example of where an older course featured a roll off toward water? I can't think of any that I saw in making my early tours of golf courses.
My response to Ira was going to be that the Flymo was invented in the 1960's, but the first time I saw it used to encourage golf balls to roll back into the water was on the 15th at Augusta, sometime in the late 70s or maybe even the early 80s.
In the late 1980s, David Ever started recommending "chipping areas" around greens at fairway height for various USGA events, and in the 1990s, some of those short-grass areas were added to bring a water hazard more into play. I think Mike Davis was one of the main proponents of that. The one he added behind one of the greens at Torrey Pines [so a ball that went over the green would go down into the canyon] was particularly daring, or egregious, depending on your personal opinion of them.