Feasibility of Integrating Proof of Stake systems into everyday devices?
The use of other devices to mine bitcoin probably came from the desire to do something useful with the heat that mining creates.  It takes a lot of energy to slow cook a pot of chili, so the thought was that instead of using traditional heating elements, use SHA256 ASICs.  Regardless of whether the electricity cost was less than the amount of bitcoin mined...you'd still cook your chili.  It was energy you were going to spend anyways, so any amount of bitcoin you mined was just an offset to your existing chili-cooking costs.

I don't think this concept translates to proof-of-stake mining, because I don't see the benefit.  Would you store funds on your toaster, which in turn proves it has a certain stake in the network?  What benefit would this provide over simply proving stake with a computer?  When there is no heat to find a use for, this concept falls apart.