You typically don't close the channel after a single transaction. You leave it open indefinitely and you can route a great deal of payments through it. But you are able to close the channel at any time and get your money back.
Discussion
So, if I start to zap people, I would inevitably start opening quite a number of channels - one per individual that I zap.
That'd be an absurd amount of channels though, no?
Now you're getting it! Yes that would be a terrible network design. Fortunately you can route payments through other node's channels. You pay them a tiny fee per transaction and you can collect fees when others route through your channels.
Some nodes specialize in routing others' payments. They have to pay very careful attention to how many payments are flowing through which channels. They have to balance fee rates and try to gauge which nodes are reputable and well connected. It's basically a whole job unto itself. For the purpose of sending zaps you can just open a channel to a routing node and not worry too much about fees. One channel should be all you need.