Moon 'sighting' is much earlier than the Islamic tradition. It's discussed in the Mishna, so it was at least debated in the 2nd century CE: https://www.sefaria.org/Mishnah_Rosh_Hashanah.2?lang=bi

The charitable case is that while something might be predictable, it's our conscious interaction that's important to these religions, not the theoretical knowledge.

The uncharitable case is that religions derive a lot of power from being able to fix time, and this demonstrates their sovereignty over people's lives in this sphere.

I and many others use calculations but some folks prefer the traditional method

Ah so it is just a preference? Is there usually an actual difference on when Eid is between the final "traditional" observation and the predicted calculations?

There are no official Muslim institutions, most people follow their congregation or teacher. The choice of who or what to follow is also a personal preference.

lunar groundhog day!