This blog post is a really good argument. The kicker for me was that we all generally switch to rounding when asked for the hour (without minutes) but don't round when asked for the minute (without seconds). That's an inconsistency for which there doesn't seem to be a good reason.

However, this inconsistency only exists orally. When a device displays the time, it never rounds. Changing the convention would probably be very confusing for a lot of people, at least initially.

For now, I'm convinced that when communicating the minute orally, I should round to the nearest minute, just like I do with hours.