I assumed you'd be breaking the units into tenths all the way down, not quarters as you advocate here. Would certainly solve the problem though, maybe even too well.
The units are based on 10, but nothing stops people from dividing it further. Just as someone might use a unit of "half a kilometer" or "half a liter", which are other base 10 units.
After giving this some more thought, I realize you're right. We already deal with programs starting on xx:30, now we'd just get used to things starting at x.25, x.50, and x.75. Instead of running from 8:00 to 8:30 PM, a show might run from 8.00 to 8.25.
6 minutes is too much time though, if you tried to fill that with ads you'd lose your audience fast.
Dividing into thirds doesn't really work in a decimal system.