Decimal seconds are slightly shorter than normal seconds, so times that use seconds are more precise. The other fun thing is that decimal time doesn't really need names for the levels, it's just numbers of significant figures so if you only want to give the first digit of the seconds that works too.
It's less precision for a given number of symbols. Fewer usable factors mean you can only reasonably divide up segments of time into larger, less precise chunks.
This is far from the truth. The closest time before midnight you can conveniently represent in the current time system is 23:59:59 which is six symbols for a standard second before midnight.
In decimal time the closest time before midnight you can conveniently represent would be .9:99:99 which is noticeably closer (0.163 of a second closer) to midnight and uses only 5 symbols.
This should not be surprising - our current system is very inefficient in its use of digits.
45 minutes and 00 seconds is very close (less than a quarter of a second difference) to :23:33. But there's no magical or particular reason why 45 minutes is an important time period to make a nice round number. :24 is a very convenient number (so many factors!) that's very close to the same time duration. That's 46.2963 minutes.
Or maybe you are referring to three quarters of the way through the major division. That's actually pretty natural too :75 like a percentage. Now dividing the major division into thirds is a little less convenient but I do that far less than I need to add and subtract times which this system makes much more convenient.
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
