If I have to go with what people tell me my most popular piece has to be this one A minimal email client – Manu
Soooo many people found my blog thanks to that post. Go figure. But I get what you’re saying.
In browser search can only look for titles though. Inside the archive that is. An actual search (and search engines) can go through the content itself so that’s obviously a lot better.
I don’t have a threshold. A lot can depend on how good, or fine grained, a blog’s categories and/or tags are.
But I can give you an example of a very large, very subject diverse blog which is improved by having it’s own search:
There is another problem with relying on a third party search engine to search blogs: Google and Bing routinely let older posts drop out of their indexes. ie. some blog post from 2007 may not stay in their index unless other’s have linked to it.
My personal opinion is “yes” because it’s a neat feature that I find myself using quite often. Both on my own blog and others. At least if the blog has a decent amount of posts.
I often come back to blogs and might not remember the exact title or category or tag and then the search box comes in very handy. And especially if some time has passed so I know the post I’m looking for is deeper in the archives, then the search can save a lot of scrolling/clicking.
My own blog has a huge archive going all the way back to 2009. Tags and categories aren’t near enough since each of them has a ton of posts in them by now. I NEED search, haha! If for nothing else so that I can find my own posts 
Sure people can use Google or download the site or whatever, but it’s an extra step that most people probably won’t bother with unless it’s something super important. I already use WordPress so I include a search box just to make life easier should anyone have use for it.