Thanks for the example.  If you were to use a smart contract, then Bob would have not have the option not to pay.  A smart contract would be set up so that when the bet was placed, funds would be placed in escrow meaning that the winner of the bet would be paid automatically depending on the weather the next day (as you can appreciate, such a bet would not be ideal for a smart contract because there needs to be an automatic trigger for the contract to execute).

Giving another example - a good use for a smart contract would be between a consumer, a supplier and a delivery company.

The consumer places an order and has funds in escrow.
The supplier sends to the delivery company for delivery
The delivery company delivers and obtains an electronic signature

The signature is the trigger event - it would trigger the payment to the supplier.

I hope this helps.  The thing is, smart contracts, the blockchain, the whole technology is still emerging and being discussed.  There is no real right and wrong use for a smart contract at all.  It is just thinking out how it would work.

Using the example you gave, it would work if there were some kind of electronic sensor/weather station that can trigger the payment to either Alice or Bob depending on the weather at a certain place at a certain time.