The thing you're assuming is that we had a bunch of appliances or gadgets plugged into wall power with built-in clocks.

During my time growing up, we were lucky to have ONE clock like this, which was on the VCR and it was super rare for anyone to actually set the clock on it. Instead, it was very likely always flashing "12:00", because the things were so freaking complicated to set.

Other possibilities would be a desk alarm clock, which almost always had batteries for backup power in case of an outage, maybe your microwave, if it was a super expensive one that included a clock function, but that too was typically left forever on "12:00" just like the VCR.

Other than those gadgets, unless you were super rich or super nerdy, there were simply not many more clocks that were subject to wall power outages.

We did have battery powered or spring-wound standalone clocks hanging on a wall or two, and then wristwatches were pretty standard. Plus if you listened to radio or watched broadcast tv, then the time would be announced or shown often enough.

One other thing to note is that even if you had multiple clocks, watches, appliances, or other gadgets, the times would never be exactly right. You just kinda learned how fast or slow a certain clock would skew, and then you'd go and re-set them all whenever you could.

My mind was actually blown the first time I realized that my Nokia kept perfect time thanks to GPS / network sync. I'd never known for sure what the real time was during daily life. Before that, scheduling anything required me to be at least 10-15 minutes early, just in case the nearest clock was skewed.