Your job is more than just code. Your job is other people too. Live in a box all you like but you're completely discounting the value of ensuring other members of the team know what's going on with you over your current work item.

FWIW, imagine how a greenhorn might feel working on a team with you. If you feel like giving them some time of your day is a waste or that listening to their problems is a waste they're not going to feel enthused working on your team. Sure, that doesn't necessarily influence your current work item but it might contribute to overwork later if they leave for a team that actually makes them feel like they matter.