Elo chess ratings are accurate to the point of meaninglessness

Here's some questions:
Is there definitely a difference between a 1000 and 2000 rated player that are active?
1500 and 1600?
1800 and 1850?
1900 and 1901?

I argue that having a fourth digit in a chess rating conveys no meaningful information. It is not at all certain whether an active 1900 is better or worse than an active 1901. I could turn my blitz rating of 2058 into 205 or 206 and basically nothing would be lost. Cut off the last digit, it's insignificant and is too precise for the thing we are measuring.

Ratings are designed to predict game outcomes. They do that by looking at past performance.

It has nothing directly to do with how good people are, but instead how well they have performed in the past.

Every chess rating, at every chess site, is perfectly accurate, just like the Seattle Mariners record of 59 & 54 represents their baseball performance this year. They're mathematical formulas that summarize the past.

Your argument is like suggesting that batting averages should be rounded off to the nearest 100.

Elo goes beyond 4 digits, it gets to decimal accuracy behind the scenes but is rounded off for simplicity. Why round off those but not the ones place, which seemingly is also too precise.