They do (well partly), but with network level blocking you end up with broken DOM elements (like images, videos, etc.) The good think about the browser extensions is that they clean up the DOM and in many cases you wouldn't even know if the pages had ads.

Then there's also Javascript trickery loaded with the page that do hostile things if ad servers aren't reachable, and extensions know how to detect and replace them.

I think the closer the blocker is to the user, the higher the fidelity of the blocking.

A browser extension has access to the actual requests, while all a network level blocker has is the Server header of a TLS packet at best, just an IP with SNI encryption at worst. That's why PiHole works as a DNS proxy by only properly responding to non-blacklisted hosts with a proper DNS response, but even this might be useless in some cases due to "domain fronting".

A PiHole only sees the DNS request, which works fine if ads are served from a separate hostname like ads.mydomain.com. But if they're served from the same sub-domain and simply have a different URL (ie, mydomain.com/ads/[...]), then the PiHole won't block it. uBlock/ABP will, because they can filter on entire URLs, not just the domain.

uBlock (and AdBlock Plus) can access and prune/block individual DOM elements, and even has a built-in tool (the eye dropper icon) to select and block them. I think they call it "cosmetic filters". It's also available in the right-click context menu under "Block element".

I don't know exactly how it works under the hood, though. If I block a div with text in it, I know the div is still downloaded, just not displayed. I don't know what happens in more complicated cases, like if I block a div that contains an img tag. I think it's smart enough to prune the img tag before the browser downloads it, but IDK for sure.

I vaguely recall Privoxy having some kind of content filtering, but when I tried it, it wasn't html/css/javascript aware, and only did regex based replacement.