Imagine the reaction a person from the 18th century would have if I told them it's silly to burn things to make light. You're the 18th century person in this scenario. You have never seen an incandescent light bulb, let alone an LED so I'm clearly crazy right? Of course you burn things to make light, how else would it be possible?
There is no need to send your password to somebody in order for them to authenticate you as someone who knows the password. Symmetric PAKEs which do this are actually relatively common in new systems that had a cryptographer help design them today, Bob knows the correct password is "Sesame" and Alice tells Bob something which proves to Bob she knows it too, but even if Eve hears everything both of them say she doesn't learn "Sesame" and won't be able to satisfy Bob that she knows the password.
For real human passwords, verified by humans, like "What's my favourite vegetable?" there's a wonderful protocol the Socialist Millionaire's Protocol, which lets you play this out, each participant says what they think the password is, and the protocol tells them both if they gave the same answer. Because humans are in the loop this can use low quality passwords, if I try to "brute force" you by guessing every possible vegetable you'll get sick of me wasting your time and disconnect.
Better yet, asymmetric PAKEs make it possible for Alice to tell Bob a fact which Bob can use to verify that Alice knows some password P, but without Bob knowing P. Eve can hear everything they say and still doesn't know P and can't impersonate Alice.
This stuff is almost as old as the World Wide Web.