Dwanyin,
Your observations are correct I think, but there is a tendency in the type of representation we see in these paintings to show fewer details in the less important people's pictures.
Personally I think that there are two types of bows used in the Ming dynasty, the long necked (long kasan in Turkish terms) and the short necked (more like a Turkish or Persian bow). I feel from the paintings I have seen that there are probably string bridges used on both, but they are of the flat Crimean Tatar form. These are easily omitted in paintings.
The lack of them in a depiction is incidental to the fact that they clearly were know and used on some bows. There is no reason to assume that in a country the size of China they were used on all bows since there are viable alternatives. The Turks and Persians lived next to each other, but used different approaches to string bridges.
