What's the advantage of using a completely separate blockchain here over some kind of asset or token?
The main point of dividing up applications into separate blockchains is to prevent centralisation (which will always eventually result in corruption IMO). It also makes it easier to market something that isn't trying to be everything (a problem that Qora currently has IMO).
If you look at the way that the world-wide-web has currently evolved we have multiple "application platforms" rather than just one "this is everything" web-site (i.e. that's why you are using BCT rather than Google for your posts).
I have been against the idea of Bitcoin been "the only blockchain" as well (part of the motivation behind the design of AT to be able to function as a way of being able to communicate between blockchains).
Also certain applications will prefer faster confirmations than others (not really possible if you want to put them all in the one) and others might actually be geographically limited (which will be able to work much faster because of that).
It's also a bit like what NASA does with a spaceship - it has multiple redundant systems so if one system malfunctions you don't end up with a catastrophe (by having all blockchains support AT then in fact all applications could be run on any one of them although it might not work as nicely on a blockchain that was designed for a more specific purpose).
In regards to voting I am not interested in a POS approach and the alternative requires a different kind of mechanism to control account creation (which I've been working on for some time now). When you have such a fundamental difference it makes sense to create a different blockchain (rather than to try and add that as another feature to the one blockchain).