I'm guessing that having a tick for longer than 24 to 48 hours was a clear enough reason. I assume people who get hundreds of ticks will be checking more thoroughly and remove them within two days.
I agree antibiotics shouldn't be prescribed without a clear reason. People are being prescribed antibiotics all over for things like the common cold and for some insane reason we're still putting antibiotics in farm animal feed.
But it seems unethical to then take a gamble on whether someone contracted Lyme disease or not just to give the antibiotics we save from that gamble to someone with a runny nose. If we want to save antibiotics then we should test the removed tick for Lyme disease, not wait for symptoms to appear.