I'll throw my hat into this potentially old ring.

While I don't think that you HAVE to do cleans and jerks (or most likely push presses) I think that they are hands down one of the best exercises to increase overall power and athleticism.

No other lift has the ROM that clean and jerks have. That alone is a huge plus. Taking a weight and moving fromt he ground to as high as you can lift it overhead... huge distance and huge amount of work to get it there. You could get this ROM with something like a weird deadlift/upright row/military press (or SLDS/reverse curl/military press) but in the end, part of the beauty of a clean is the speed and power it develops. It is the speed with which that distance is covered that is the real key to the benefits.

One of the best things I ever did for my shoulder strength and development (not that development is a major concern of mine, but I thought it would be an interesting note to some "bodybuilders" around here) is to ditch strict pressing and hang my hat on push pressing and jerking... Olympic Jerking