Is there any economic benefit at all to the network from such a mining? The transactions are practically handled centrally, like in banks(?)
No, it's distributed. (Unless you think Bitcoin is also mined centrally, due to a few mining pools having a virtual monopoly.)
Does it [PPCoin mining] function in absence of a central authority? If not, in what way is it distributed?
SlipperySlope reported in his PoS alt-coin development thread that a bitcoin core dev said this:
The problems to address as viewed by a member of the developers email list . . .
The problem with proof of stake is essentially that there is no cost to
creating a proof-of-stake.
...
The problem is what wrecked Peercoin, which I understand is now
centralized (all blocks are signed by the developers to be valid). ]
I cannot vouch for the accuracy of this information, but it sounds like the fact that shares are free to create caused a problem that forced Peercoin to become centralized around the developers who sign each block to be valid. So in essence, these developers are the "Central Bank of Peercoin."