The core of it is getting closer to true "reactive" programming. If you use hooks right™, you generally don't have to worry about how to handle values over time. React does all that plumbing for you (which is why we need all the dependency arrays).

This for me is the main advantage over class components. You don't need to worry about the various lifecycle methods (including having separate methods for componentDidMount and componentDidUpdate and making sure you do all the plumbing right when your parent changes props that you weren't expecting).

IMO, React really could have benefited from devoted language syntax for this (like Svelte does) to automagically and statically track all the dependencies. But React has an ethos of being "just JavaScript" (even JSX desugars to relatively straightforward React.createElement calls, and you can treat those nodes like regular JS objects, pass them around willy nilly, etc.), so it didn't happen (and instead we have lint rules like ESLint rules-of-hooks that are designed to enforce the invariants that really the programming language should enforce).

Edit: The other nice things about hooks is their composability (and this is in fact related to what I said above). With class components, a component can have one state object, so it's hard to compose with other "mixin" type behaviors that need their own dedicated state. You ended up with weird patterns like higher order components (à la Redux withStore) that have basically ceased to exist with hooks (replaced by a useStore hook which can opaquely manage its own state under the hood).