"Not wanting to run your own server" is not the primary issue. People might run their own servers if it was as easy as running a Mac or a smart phone.
People hate manual IT and system administration. They will sacrifice money, freedom, privacy, control, even ownership of their own works to avoid having to futz around with that stuff. They hate it that much.
(There are a small number of people this doesn't apply to. These are called enthusiasts. There are also car enthusiasts who like to change their own oil or even rebuild their own engines. We are talking about 99% of the market here though. Enthusiasts are a small niche.)
It's easy to understand why if you count time as money. Lets say you value your time at $60/hour, which is probably on the low side for people here but lets be conservative. Now lets say you have to spend three hours a month messing with your servers. That means it's costing you $180/month or $2,160/year. That doesn't count the additional cognitive load of having to worry about it or the inconvenience of something going down and needing attention at an inopportune time.
If those issues were addressed, you would see more people running their own servers. Unfortunately the "ease of use is for stupid people" meme goes way back in tech culture:
http://catb.org/jargon/html/P/point-and-drool-interface.html
^^^ This is why FOSS has never crossed the chasm. It's a cultural problem.
Another contributing factor is the love that some developers have for complexity. They see complexity as a sign of intelligence. It's not. Simple systems are far more difficult and require much more intelligence than complex systems.