Earlier quoted context omitted.
You're gravely generalising, as if everyone who does side projects has to do them the same way you do. And even disregarding this, you're still not proving my point wrong. You're saying personal projects show you can work in some set of conditions that have little to do with how work in a company gets done. Yeah, you can "prove" yourself somewhat when you're on your own, does that automatically translate to being a g…
As an employee you do what is assigned plus administrative things. That is incredibly limiting. On a personal project you accomplish whatever you want, regardless of demand or ambition or challenge. You are your own principle audience. You aren’t trying to prove anything. You are trying to build something. Unless you are the kind of person just likes building things I suspect it will be impossible to understand.
For the record, I am someone who just likes building things. I totally get why building things on your own is more enjoyable. I just don't think that an employer really cares all that much about that.