why does plugging into a new USB port often solve USB problems?

Solution 1:

I suspect you are having power problems. With that many USB devices, some hubs can be overloaded and won't enumerate correctly. Moving to another port probably moves it to another hub which has sufficient power. The solution I have found when I've had these problems is to go get a powered external hub and plug into that. That has solved my enumeration problems every time so far.

Solution 2:

Some drivers and applications cache port infos and try to access the USB resource always in that location.

That is definitely the case with my UMTS mobile USB stick. The port I used the first time is now the only one that works.