People, corporations, and other entities would over time gather more data about you. There’s always some kind of information footprint that you leave behind. And you’d stand out from other humans by the way you talk (i.e. using slang from 200 years ago, and speaking about historic stuff with details that the general public is not aware of) and other traits, which makes you traceable.

You’d procrastinate things for 100s of years, until at one point you’re simply no longer able to do it. Wanted to domesticate a saber-tooth cat some day? Too bad, they’re extinct now. Wanted to visit the baths in ancient Rome? Well, it is not the same Rome anymore, and all the baths’ floors are cold.