The angular velocity originally is 6.283 rad / 86400 sec = 7.272205216643E-05 rad/sec

No it wasn't. Prior to the introduction of leap seconds we didn't have time synchronised anywhere near as well.

We didn't care about the leap second.

When we decided to make it all official and rigidly set, atomic clock times were already 10 seconds ahead, and we just stuck that into the definition. Atomic time is currently 37 s ahead of UTC, the 27 leap seconds and the 10 extra seconds.

It was only 1955 when they started using them and 1958 when they set it to try and match an equivalent of UTC, based upon impefect observations. Leap seconds were introduced roughly 10 years later (technically 14, with 2 leap seconds added at the start) and UTC was set to 10 s ahead of atomic time.

This was also done without taking into consideration gravitational time dilation, meaning the various clocks used were ticking at different rates. So atomic time wasn't even counting the seconds exactly.

This indicates that even during that time, the Earth was still spinning at pretty much the exact same rate.

If you did want to try and figure out a day that was 86400 s 1972 is not the right year.

Instead it would be based upon what the SI tried to model it off, which was Dec 31st 1899.

But even that wasn't constant as it shifted what it was trying to model, first making a second based upon one fraction of a tropical year, then using a slightly different fraction, before just setting it to atomic time.

So even then you likely didn't have exactly 86400 s in a day.

So while the math may be correct, what you are measuring/assuming is not.

We simply haven't been measuring atomic time for long enough to be able to try and develop an empirical model (i.e. one based purely upon the numbers) to try and figure out how fast Earth was spinning ages ago. You definitely wont know if it is linear or exponential or logarithmic and so on. They all approximate linear functions for small scales (every continuous function does).

If the earth did not slow down, then both the Atomic time and the Universal time would be in sync.

Only if they started based upon the length of a day being exactly 86400 s, which it didn't.