I'm a System Administrator by trade and would not ever recommend a solution like this. Centralized systems are just easier on the user and much more cost effective.
Think about how many professionally developed websites fall prey to SQL injections, CSRF vulnerabilities, server exploits and the like. Nginx recently issued a warning about a big vulnerability in all but the most recent version. Github got owned by Egor Homakov using an old Rails exploit.
And those are professionally maintained. When your average "I'm not computer-savvy, but I can work Microsoft pretty well" user is the one setting up and maintaining the server, how long do you reckon it will be before somebody takes over his computer? My guess is that you're very optimistic if your answer uses hours as a unit.
Take for example an AI that watches your facial expressions and helps you around the house. It might be cheaper/easier to have the computation happen locally and avoid the cost of streaming all of that data to a centralized location all of the time. Then again, having all of the data in one database may provide the AI with enough benefits that it is worth sending it across the wire - with aggregate data, valuable aggregate patterns can be found. It's hard to say at this point.
I have a really hard time seeing people buying a box to support the next facebook ...
what if it would be the next web?
I currently have a home server, but my career is in information technology and my wife is a photographer. In my case, we have the need to have a central place to store all of our files so that they can be backed up regularly. Even being an I.T. guy, it still took me years of thinking about doing this before I ever did it. I love it now that it's in place, but when there are problems with it I'd almost rather just go back to living on the edge and storing files on our various computers than having to deal with the problems.
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Serverless, encrypted Chat & Filetransfer
Multiple simultaneous downloads / uploads
Search Friends
Messages
Forums
UPnP / NAT-PMP port forwarding support
GnuPG Authentication
OpenSSL Encryption
Plugins support
Graphical User Interface written with Qt4 toolkit
System tray integration
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For every pro in any solution there's usually a similarly weighted con, both of which need to be balanced against the users technical ability, requirements, "infrastructure", etc.
There's no such thing as a silver bullet, but it's what makes the game fun.