This "personal computer" thing will never work.
First of all, people will have to maintain the hardware. Can you imagine your average user doing that? The average CPU would probably catch fire from dust build-up if non-system-administrators were put in charge of them. Each individual "PC" owner would have horribly low purchasing power, too, so any time one of these personal computers broke, they'd have to pay a ridiculous one-off retail-unit price to get a new one. No volume discounts!
Second, these machines wouldn't be near network peering points, like colocated machines are. They'd have horrible network latency and throughput, and a lot of residential ISPs wouldn't even let you talk to them from anywhere else. How would you get your data from your home, of all places, when you're at work? Can you imagine what horrible BitTorrent performance they'd have compared to the standard cloud seedbox?
In fact, there would almost certainly be times when they're either broken, or just switched off. Which means that these "personal computers" wouldn't be highly available like our everyday cloud-agents are, so other services couldn't rely on anything like webhooks to communicate state-changes with them. With enough of these "PCs", services would likely be architected with this "might be broken/off" model in mind, providing only RPC-based protocols, and disallowing pub-sub altogether.
And without push-based data delivery, you'd lose half the point of having a personal machine-agent: keeping data intended for you stored safely on your machine with your encryption, instead of leaving it buffered at the sender.
Why, I bet you'd see companies sprouting up to "serve this need" by acting as intermediaries, where instead of your friends directly pushing data over to your agent, they'd send them to the intermediary's agent, who would then wait for you, later on, to come and actively retrieve them using your "personal computer." And I bet that with such an important place in dataflow, these intermediaries could convince people (these poor people) that it's safe to just encrypt the messages with the intermediary's private key, instead of the receiver's! Automatic agent-to-agent peer-based crypto might never take off at all, and we could see some centralized system based on trusting rich companies to hold your data where anyone from some advertiser to the NSA might snoop on it!
...but I'm being ridiculous. Surely things couldn't get that bad.