That's an interesting idea, but it could be argued that this assumes that all of the world's timezones will agree to observe the same set of leap seconds as they currently do.

Otherwise, it shifts timezones from being 15 minute granularity to 1 second granularity. Not technically impossible, but will definitely make cross-boarder meetings interesting once the discrepancy becomes large enough. I feel the 15 and 30 minute timezones are already bad enough.

Because then one day you wake up early in the morning to find the noonday sun staring at you. It will take a while though. On second [heh] thought, you might not wake up. But some distant relative would.