Does it make sense to power multiple 12V devices from one single power source?
The idea has reasonable merit.
No utterly major show stopper but things to think about.

The arrangement is non standard. You need a 12V distribution hub with appropriate sockets. These MAY vary between devices. You could always replace plugs that do not fit your standard but this is annoying at least.

You still need all the cables. With mains feed to plug-packs you can cluster the groups of packs but with your scheme all power cords must reach your hub. You could have sub-hubs but then risk voltage drop due to extra cabling - voltage drop is higher at low voltage for the same power. 

As PlasmaHH says - adding single point failure mode is undesirable. Worse, as he also notes, if the psu ever went high-output you could have a grand Y'All come peripherals barbecue. Or worse.

I have about 20 x 12V devices in use here  - mostly multi Terrabyte hard drives.
A substantial open cage supply may be rated at 12V, 250 Watts - or about 20A. Many devices use a 1A x 12v supply but some use 2A or 3A supplies. So in my case I'd need at least 2 x 250 W supplies. YMMV.

I have never had a plugpack fail in my "hive". I have shelves of external drives or other equipment with plug-packs on a lower shelf close to their drive. Cords can be neatly tied. Various spiral or apparently spiral plastic sleeves can be bought to tame the wires.