What is the benefit of writing lecture notes for an introductory course vs using a textbook? Background: I am a junior university staff member, and I will teach an introductory course in linear algebra for the first time in a few months.

I see that many teachers devote time to writing lecture notes. To me, this looks odd. Whatever I can write will not be half as good as a well-written textbook. so my first choice would be looking for a good book, recommend it to the students, and stick with it as much as possible for my lectures. "Everyone writes their own notes" looks like a model in which there is a lot of needless duplication of work.

Why do people write detailed lecture notes for basic courses? What is the advantage with respect to following closely a textbook?

Are the two approaches really alternative, or am I misunderstanding the role of lecture notes? Should I do both?
As someone who's tried to do both, there are some very valid reasons to prepare "formal" lecture notes.

The primary reason why you'd want to create your own notes is that for many courses, a single good text is not available, and as a result, the instructor has to cobble together material from a number of different sources to produce a coherent set of lecture notes—or recommend that students work with multiple source texts. (Given the out-of-control nature of textbook prices, the latter alternative is unlikely to work out well.)

If you have a single-text class, it may not be necessary to provide students an additional set of notes, provided your lectures stick to the main text material. However, if you bring in alternative or additional topics into your lectures, you may want to include notes for those topics, and refer students to the textbook for places where you follow the "standard" outline.