How close do you want to get? For what purpose are you representing 12:15?
.5:10 is 12:14 and 24 seconds. That's pretty close and uses only 2 sig figs - even fewer than the four you needed to represent 12:15.
But also, why would you obsess about these specific times? If we were using the proposed system and someone made the argument to switch, you'd be saying 'How well does your system represent the time .5:1 ? It's only 2 sig figs, but you need to go down to seconds to accurately represent it - 12:14:24.
It can get worse too - .5:01 is 3 significant figures, but to represent that time in the current system requires that you go down to tenths of a second with 7 significant figures - 12:01:26.4. Or if I go down to second equivalents, you sometimes need to go down to milliseconds - .5:09:01 is 12:12:58.464
