Well, it seems there's a bit of a controversy going on here.
One group of people seem to think that the experience of playing can actually teach you new ideas, and that's how you can best improve. There's certainly pedagogical research that says a sizeable portion of students learn much better by doing than by observing/listening/reading/viewing. But that's not true for all students.
Another group seems to think that training (presumably regimented instruction) is the way to improve, and that playing undermines that. The aforementioned research states that this is true for a different segment of students, the ones who prefer that style of learning.
There's a Third Way (and probably a Fourth...) of considering the question, though.
Almost every coach with whom I've talked, or whose publications I've read, advocates using play to improve because:
It is the primary diagnostic tool for figuring out what the player is doing wrong or doesn't know, and
It reinforces the concepts already learned in the instruction
You'll notice that they're not saying that you should play games and try to take notes afterwards on the good new stuff you found in them.
It's just that, in their experience, you can't improve very well solely from instruction. You need to practice, and to be tested. Your mistakes are the evidence of areas you need to improve. Playing reinforces newly-learned material, and highlights when it hasn't been properly assimilated.
And incidentally, I've learned plenty of new ideas and maneuvers over the board; it'd be amazing if you never saw any in your games, and surprising if you didn't notice at least some of them. In some cases, during a game I struggled to find an idea, and failing to do so, was inspired to look for the theory and examples afterwards, using some games from a database. That's something I wouldn't have done without having the experience of needing something I couldn't come up with while playing the game. So "play as instruction" has certainly applied to me.