The point is that at the moment, a day has 86400 SI seconds. If you want to keep it that way, i.e. change neither the length of a day nor change the length of a second, you will have to either divide these 86400 SI seconds up into some sensible pieces (60 60 24, e.g.) or have some remainder left (one day of 10 hours and some weird stuff at the end).

The problem here is not the one-off second, but the length of the second per-se which would have to change. Unfortunately, the length of the second is so deeply tied into the SI system that I’d rather have a non-metric day than a change in the length of seconds.

Timezones are somewhat orthogonal to this, and while there is some advantage to having a global time (‘let’s meet at 17:00, okay?’), local timezones are also somewhat helpful – you can expect shops to open around 8:00 all over the world and wouldn’t expect them to be open at 22:00; similarly, local authorities can change the time (and hence the time when shops open/close, e.g.) without everyone having to reprint their opening times signs (as happens for DST or during WWI/II).