Love the idea of logging time spent. I do the same. Care to elaborate on what you mean by 'fake work'?
Examples:
0) On my company's mobile site, the navigation header wasn't centered. I almost spent time fixing it until I realized it literally didn't matter
1) I'm using some open source code in my MVP, I almost went through and cleaned up the code - but it worked without doing so, so why would I take the time to?