I suspect the only part of the Masters people object to is the ultra pristine conditioning; causing other Clubs to try and emulate those conditions. Could Augusta National achieve those conditions if they stayed open all year long?
What are the differences in conditions between AN and ACC? Does it make it that much easier to pimp out the Course by shutting it down over the summer? Or is that choice made for different reasons?
To answer your question, they could acheive good conditions most of the year-as do many clubs that overseed.
But there are tradeoffs and it depends upon when you want to peak.
If they were open year round and chose to oversee wall to wall, which they do, they would have an ugly transition period in late may or June depending upin how long they chose to hold onto the rye.
Rye grass is green-it's not over watered-it's just green.
In the summer,the underlying bermuda would emerge and it would be a lighter shade(after the rye turned brown and died off)
Constant overseeding can take its toll and many clubs alternate(generally because they see the downsides and forget the upsides of overseeding and not overseeding) Whether they do in a specific year goes in cycles depending upon when a club wants to peak, who's in charge, and when that guy play the most golf.
Palmetto has made the decision to be mintin April for The Masters(firrm and well drained Wednesday even after all the rain of Monday/Tuesday) , and they are mint via overseeding most years, but they are pretty good most of the rest of the year after a brief transition in June, then an overseeding period in early October.