Isn’t it the opposite? If you lack time management skills you need to constantly be aware of the time, while someone else does it without having to, and without needing to spend mental resources on it.
Ah, but that’s how you DEVELOP those skills in the first place. That’s the trick. They didn’t magically wake up knowing the movement of the clock gears. This is an unnatural state of mind. A forced mental distress.
People are different. Some are born with a working internal clock, some aren’t.
But time management is more about knowing how long you need to do activities and planing accordingly. You practice by doing an estimation, do the thing, see how long you took and next time correcting accordingly. And there is no shame in using alarm clocks to remind you of the important bits.
That said, mental conditions like ADHD can make this incredibly hard. But in general you don’t keep the clock in your head, you keep stuff in your head and look at the clock every now and then.
By that logic, any social skills are an unnatural state of mind. Or learning math. Or anything that you weren’t born with
