Doesn't seem like such a bad idea to me. There are plenty of times when it would make things a lot clearer. People often refer to the early morning hours as part of the previous night instead of the current day's morning. For example, someone might say, "I have to catch the 1am train on Thursday." Are they talking about Thursday morning or Friday morning? "I have to catch the 25:00 train on Thursday" is completely unambiguous.
At any rate, I can think of dozens of really goddamn stupider things we do in the US. Using English units of measurement, pricing things X.99 (and not adding in the sales tax until checkout either), etc.