Rick:

All of your points are valid and well taken.

Correct me if I'm wrong, but I believe what you are stating is the ancients not understanding/using the decimal equivalent of this ratio.

What is missing in your post is the view of its daily use.

When I was a young lad we were taught how to use a slide rule from grade 12 through university and pi was always 22/7...we couldn't calculate any closer with those sticks...not even the best on the market (Picket). So anything beyond the accuracy of two decimal places is unnecessary, unless your work requires closer tolerances.
The ancients wouldn't have calculated the value as a decimal; they would have drawn a circle of large proportion and measured its circumference physically.
As an example:
If we assume they setting out a circle of diameter 100 cubits/units then they would measure a circumference of 314.2 units. Give them a little credit...they could measure accurately…Giza proves it.
Unfortunately they couldn't do anything with this number since they worked with fractions on a daily basis so they simply "fiddled" with the 314.2/100 ratio and ended up with what I used in school...22/7...a ratio developed many thousand years past.

This web site has discussed the pi as an ongoing issue...there is nothing complicated in its measure...once you understand the relevance of how and why it is required. But the use of modern calculators is what we now understand...it's all that the average individual uses because fractions have been tossed out the window…unfortunate but true !

Best.
Clive