Let's assume you're in NYC. That'd UTC-05, so midnight UTC is 7pm local. If the timer is reset at midnight, it is true that you could do one test at 5 pm and another at 8 pm during the same day, but in a given "UTC day" you can still only do one. In other words, if you do "tomorrow's" test at 8 pm, you still need to wait 23 hours for it to reset at 7 pm local before you can do another one.
It's no different than someone in London (whose local time is effectively UTC) for whom the timer would be reset at midnight local, except that people not on UTC would have it happen at a different time of the day.
The advantage would be that if one day you are late, you can do it earlier the next day. Right now if you do it at 10 am, you have to wait until 10 am of the next day to do another one. You have to essentially be on time and it'll still be pushed forward on the clock every day, and sometimes it's easier to just skip a day in order to do it early the day before so there is room to add a daily delay to it.
Flickr does exactly that: at midnight UTC, all the counters are reset. This means that if a group has a limit of 3 photos per day and you have posted 3, you only need to wait until midnight UTC to have your 3 daily slots available again. The same thing happens with the statistics, which mark a new day at midnight UTC. In my case, since I'm in Italy, this happens at 1 am. For someone in Memphis, it happens at 6 pm.
And yes, I'm probably just being a pain about it. It just surprised me that the required interval was 24 hours since the previous test, rather than "one per day" as I had assumed: to me (and I imagine to most people), "daily" means "you do one today (at any point during the day), and then another tomorrow (at any point during the day)."