There are protections in both cases. But they are different.
For instance, in the USA, there is no requirement that you have a mechanism to provide information stored at home to law enforcement, even under warrant/court order. If you have one, they can compel you to use it, but if you don't they have no remediation.
But a cloud provider is legally required to have that mechanism, and when order if they don't exercise it, they are punished. See: https://en.wikipedia.org/wiki/Stored_Communications_Act and https://en.wikipedia.org/wiki/CLOUD_Act.
If I had data that I legit feared the government finding, I wouldn't be protecting it with a home server - I'd protect it by encrypting the crap out of it and storing it on a pretty generic cloud service, not in my home or anything easily traceable to me.
That's not really what Solid is about. Solid is not just about me, it is about us. The stuff we do together. The sharing we do, but we share not just with anybody, but with someone we trust. It may be something really trivial: I share my grocery shopping list with my wife. It is not sensitive by any means, but it is also nobody else's business. Those are data used on my terms. Nobody should be peeking into my life to map me, as I go along with my daily business, but my daily business consists of interacting with a lot of people, and I do share and I want to share, but I want personal data control.
Now, personal data control is really the key to permissionless innovation. So, we're not just doing it to protect from snooping, once people have their data then you get a level playing field were there can be competition for the best user experiences.
