The points that Andrew makes are valid and important. Styles act a bit differently in tables.
I concur that simply applying the Table Text style, which is Arial 10 pt does NOT change the font size in a table.

I am going to move this thread to the Word|Tables forum.

Your sample is a bit anomalous in that in your initial table, the first column is 11 pts.

I have my QAT display style and font information directly and that is shown in the screenshot.

I resized everything in your initial table to be Arial 10 (Direct formatting) and then selected the table and saved it as a Quick Table on my machine.
When inserted from Quick Tables, it maintained that formatting and shows the Table Text style.


P.S. I agree that 10 pt. Arial is quite legible.