I have heard of many issues over the years I have spent using Picard and helping in development, but this is actually totally new to me. It is known that the UI can become sluggish or unresponsive while saving large files, especially to slow storage. But from your description this happens even while not saving, right?
There is currently work underway to port Picard from Qt4, the UI toolkit Picard is using, to the much improved Qt5. I think there is some hope this could also fix your issues. I don't know how advanced the port is or when we can expect a Picard 2.0 release, though, but AFAIK the goal was to not have years pass again until the next release