Does every hole within a golf course need to offer some form of strategy?
I think this is kind of tricky to answer. Strategy is present on every design because a golfer always has options. He can lay-up, play to the center of the green and try to 2-putt, or he can drive as far as possible, attack the pin and putt for birdie. In essence, because the golfer is able to make these types of decisions, every hole has some degree of inherent strategy.
That said, not every hole has to have a risk/reward option to it. The 17th hole island green at the TPC at Sawgrass only gives the golfer two options: attack the pin or play to the middle of the green. There is no doubt that the 17th at Sawgrass is a tough, demanding hole, but holes devoid of strategic options can also be a good birdie opportunity. In this case, they often are placed to preceed or end a series of tough holes.
Some par 3s demand a player to execute a certain shot or bail out, such as Cypress Point's 16th, Augusta's 12th and Pebble Beach's 7th. The classic strategic par 3 is the redan, originally found at North Berwick. The redan offers several options to the golfer: he can attempt an aerial approach over the front guarding bunker, or he can try to run the ball up to the green and use the slope to feed the ball down to the hole, or he may intentionally miss long and left to give himself an uphill chip or putt.