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It's meant to be a simple example. You can easily construct a similar situation for paying costs rather than activating mana abilities.

The game can't "look forward" before you announce a spell to know whether you actually are capable of paying all costs, especially when choices during the announcement of the spell like modes,...

You can always attempt to cast a spell, but the game state is reverted to the point before you attempted to cast it if you cannot complete the actions required to cast it, such as paying all costs....