The main issue with this approach for me is that Google et. al. clearly have much better physical security than my apartment. In exchange for in-principle privacy improvements and possibly forth amendment protection you take on a huge risk of burglaries, fires, floods, power outages, etc, plus of course the workload of being your own sysadmin.
Also, if you're paranoid, your data is more exposed. You can turn off all your devices with disk encryption when they're out of your control (usually) but if you turn off your NAS while your away from home it's useless. And if it's on, physical access, and therefore your data, is easy to obtain by the moderately motivated.
Google is like a feudal lord: they might own you, but they'll protect you from everyone else weaker than them.
Also, if you're paranoid, your data is more exposed. You can turn off all your devices with disk encryption when they're out of your control (usually) but if you turn off your NAS while your away from home it's useless. And if it's on, physical access, and therefore your data, is easy to obtain by the moderately motivated.
Google is like a feudal lord: they might own you, but they'll protect you from everyone else weaker than them.