It's massively entrenched because of the network effect of the themes and plugins, no doubt. What will overtake wordpress as a blog/cms platform is something that can allow for a large number of the popular themes and plugins to be dropped in (or converted silently). It probably won't happen, but think of Lotus/Excel, for example (or WordPerfect/Word) - both Lotus and WordPerfect were dominant for a long time. People converted when their data/functionality was easily imported in to MSOffice. It's not a perfect comparison, but I suspect this will be what is needed to get people to migrate from Wordpress.
Even that will be an uphill battle, given how many wordpress installs are one-click installs from control panels, somewhat customized to the specifics of that control panel's paths/security/etc.
But the thing is, many of the major flaws of WordPress are baked into its theme and plugin formats. Much like with Excel, you'll need to match it quirk-for-quirk to interoperate with it. And what's the point of simply reimplementing WordPress?
I think you could probably get away with shooting for something like 70-80% functionality via a wrapper layer around your new APIs. Even Excel and Word aren't 100% compatible between their own versions, and WP is going through a transition period where many older plugins don't work either.
The goal would not be to reimplement all of wordpress, but implement a compatibility layer suitable to emulating enough of the basics to allow some migrations and encourage people to try out something new.
There's dozens of CMS and blogging engines out there, but no one has attempted a WP-emulation layer (as far as I can tell). Although, given it's PHP nature, and direct grabbing of $_GET and $_POST and such, it may simply not be possible at all.
Even that will be an uphill battle, given how many wordpress installs are one-click installs from control panels, somewhat customized to the specifics of that control panel's paths/security/etc.