"But in practice, it doesn't seem like algorithms are used for day to day web development." Wait, what?
So there are algorithms for sort, search, recursion, divide and conquer, etc, but a lot of the algorithms are baked into the functionality of high level languages and when you follow best practices, so you don't really need to know the algorithms to use them. ...Or am I missing something?
IMHO this is what separates a good engineer from a self thought programmer. To be a good engineer you need to know what goes under the hood which affects your decisions in critical situations. So big companies are searching for developers who have great engineering insights.
P.S: A good software engineer may also be self thought I do not want to be understood wrong.