I'd say there would be a market, but probably a niche.
Personally, if such existed, I'd probably have used it in the past. Most sites I work on that want a blog, only really want it for simple purposes (ie, post stuff to the web, with maybe some comments). And there is usually a strong desire to put it inside whatever template/design their main site uses.
Packages like WordPress are great at blogging/etc, but really, if all you need is a basic blog, it is very bloated. Frankly, I think it'd be nice to have something like a single script (to handle getting/using the blog), a simple PHP include or function call to display blog features within an existing design. Etc. Though some blog software offer the ability to "plug" pieces into an existing design, most require you to build/edit/use a native template.
But really, stuff like this could easily be done on one's own (making a simple blog "engine"). Plus, making it "this simple", actually would make it that much "harder" for people with no programming/development skills.
A benefit of this bare-bones approach is also that it can be used within one's own projects. For example, most sites I work with require user authentication at some stage. It is annoying (to some degree) that a site's forums, blog, administration, CMS, etc all are separate, independent pieces of software. In an ideal world, it'd be nice if they all shared the same resources.
Things like WordPress will always be the mainstream/demand, because they provide "it all" in a single package, that a simple-minded child could easily use/administer. :)
If you're looking to build such a thing, good luck! I'm sure there will be those who desire it, and many more who won't.