[pzhon]

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In cash games as well as tournaments, you often have to fold when you would be happy to call all-in, when the fact that your opponents can bet on later streets hurts you. Calling doesn't buy the right to go to showdown. It buys the right to face more bets on later streets.

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This gets to the heart of my question, but maybe I'm being stubborn because I just don't buy your point. Why isn't each street judged independently?

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This is a fundamental misconception about poker. I've explained why. If you aren't willing to believe me, or the many good poker books which say the same thing, then you should do some calculations that you believe.