Nope, upload speed is not an issue. As I wrote before: An original image was uploaded, but there were no thumbnails.
I am PHP programmer and I have dealt with “common” upload problems on many sites and webhosts. This behavior was something new for me.
As I can say, I have found the solution, or “the main thing causing the problem” (ImageMagick lib.) and I wrote this post mainly to make my findings searchable.