I’m convinced, the accuracy of the clock matters. Your point that within one minute is on time is fair and as you said converges quickly. Definitely quicker than the life cycle of a regular clock. I’m a convert now.

That’s not true. e.g. If a clock loses time as soon as it is started (given power, wound), a time x. Then every day it will be wrong. Now, after n days it will come back around to being correct again. But, if n >> the life of the clock, then no, it will never be correct.

I can think of a few other scenarios where it’s also true that it will never be correct.

Stopped clock, a broken clock may never be right.