You don't need to consider another planet, Earth is sufficient for this question.
The real problem is in thinking of time zones as a natural phenomenon. They aren't.
Take where I am right now. I'm located somewhat west of the center of my timezeone, so my clock is 20 minutes faster than a sun-based clock. And then there is daylight saving time, which adds another hour. Does it bother me (and others) that our clocks are "wrong" by an hour and twenty minutes? Not at all. Most people aren't even aware of the concept.
Take China as a larger example. By the sun, one end of the country is 4 hours different from the other end. But unlike other countries, China has only 1 official time zone, not 5. When some people get up and have breakfast their clocks will say 6:00, while for other people it will say 10:00. But in both cases, the sun has just risen. For some people "noon" is at 10:00, for others it is at 14:00. The official clock time doesn't match the sun's clock, but people get used to it.
And as for making a planet larger, it makes no difference. We can already see that situation here on Earth.
At the equator, 1-hour time zones are about 1000 miles across, but farther north, the lengths of the latitudes get smaller.
Iceland's time zone is only 440 miles across.
Even farther north, at Alert, Nunavut, Canada, the timezone is only 135 miles across.
Stand near the North Pole (or South Pole), and walk around it. You'll have to change your watch by an hour after each step.
Obviously time zones can become confusing and inconvenient when they are too small, but in such situations (remember, the zones are an entirely artificial human invention) it's common to designate the whole area as a single time zone (typically UTC) even though it spans many, or even all, actual time zones.
But in the OP situation, everything is larger, not smaller, so, except near the poles, time zones would be even less of a problem than they are on Earth.