I'm afraid I must disagree with your 5th point, where you say "we all agree that face-to-face is the best way to communicate and collaborate".

In my opinion, commuting daily to an office to spend 33% of your time attending meetings is not what you are supposed to do as a software engineer but as a manager or team lead, where you need to understand your shareholders' requirements.

In my opinion, developers are developers because they like to code, not to attend meetings, which in most cases, I have experienced as a complete waste of my time because instead of being productive I felt like crap for not being able to produce any code for two hours in a row.

Maybe your intern was hoping to work from home to avoid all supervision from everyone else - maybe not. But to what refers to your perspective, please don't make the mistake of assuming people want to spend 3 hours daily commuting from home to the office and come back later.