If you had two rounding digital clocks, one with seconds and one without, they would switch to the next minute 29.5 seconds apart. Everyone would hate that.
Big Ben may not show seconds but people would notice if it started bonging 30 seconds early or late with new year. Which would be the case if it rounded. It bongs right on time. That kind of is the point. The news doesn't start half a minute early or late either. And people joining meetings after the minute changes in their clock are technically a few seconds late.