Good point!

I wouldn't say that I self-host in my house.   

I live in a house.  I reside in a house.  A private house.  

So my wallet is where my keys reside.

My wallet is the house for my keys.

Are my keys then self-housed?
 
Doesn't roll off the tongue, ... and does not make this all really any clearer.   But just putting that out there. 

cointastical

Can SN help Clark Moody come up with a better name for a self-sovereign wallet than "unhosted"?

IMHO, that would be confusing.  If you run software on your phone that holds your keys, you're not hosting someting.  Something remotely can't access it.  It's not like it's content, hosted for other people/devices to access.