How could a BIOS update possibly resolve this problem? Do you have some realistic scenario in mind there?
As for cables, I have used several and the behavior is always the same. This is to be expected. As I said in my original post, unlike some other phones, the Nexus 5 doesn't have a USB 3.0 port. It is physically impossible to plug a USB 3.0 cable into it. I can only use a USB 2.0 cable. Because the phone's SoC reports itself as USB 3.0 capable, this problem occurs.
What bothers me here (aside from LG/Google's apparent negligence) is that the Intel USB driver does not appear to be respecting the "Tell me if my device can perform faster" setting. This setting exists for a good reason. It's really annoying to get this useless message every time I plug my phone in, and if I'm in a full-screen application it's actually harmful because the message pulls me back to the desktop.
I do understand this can be frustrating and inconvenient.
I have noticed that the driver version you saw above (220.127.116.115) is not the one we should be looking at. You may take a look into the Intel® USB 3.0 eXtensible Host Controller for the correct driver version.
A BIOS update may include a fix for this issue allowing the operating system or driver to use the setting properly. Try searching for BIOS release notes from Gigabyte*.