1. Seam edges can't be deleted, you can only hide it. because it's the curve which forms the sphere.
2. Your sliced spheres are sliced vertically. Short lines are not seam edges anymore, they're regular lines because resulting pieces are calculated differently than the sphere thus this script is not working.
3. if you sliced them horizontally, script would work.
4. yes they return after slice because script hides it only visually. :(
5. yes this script affects whole scene. :(

Thx for the efforts!

If you slice your sphere like this and run script afterwards, it will hide seam edges

I had no chance because that is working 3 / 4 by step of 90° :)

yes or like this! ;)
But that is working only for simple objects ;)

I can also select one by one and hide them! ;)

Thx for the research! :)

Flow on a sphere