Ticks are incredibly common. People in my area of the country get hundreds of ticks during their life. It's also fairly rare they carry Lyme disease and gets you infected. You definitively should not be given antibiotics without a clear reason.
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.
I've tested random samples from a few forests in the Northeast, and >75% came back positive.