Naive finance question: why do stocks have a an exchange they are listed on if they can trade on multiple exchanges and dark pools?

You use dark pools to do large trades without affecting the market price of the stock. You don’t tip off the market making it less lightly to drive up price

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right but the question is why not do everything in a dark pool? why do you need an exchange?

The only problem is externality pricing.

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aside from the protection from regulation, is it just that exchanges offer price discovery?

Price transparency, which can make it more difficult to assess value. Also it’s difficult to detect high frauds, ponzis and insider trading

Not all securities can be traded in dark pools, only certain types are eligible, and not all investors are allowed

price transparency makes it more difficult to assess value?

The problem is that funds prefer not to have price discovery when they are taking a large position or dumping the stock. Thus they prefer "dark" venues.

Of course it would be more efficient from the economy point of view as a whole if all markets were lit. Individual traders don't like it this though.