I've been agonizing over this issue for so long, but this actually worked! Here's my story:
I got my new iPhone 12 Mini yesterday after making a backup of my iPhone 11. It's a trade-in so I did that ahead of time just in case, as you always should. I used an USB port right on the front of my PC to do it. I hadn't had any issues with those ports before. The Motherboard is an MSI B450 Gaming Pro Carbon, and of course I'm running Windows 10.
The transfer of data from phone to phone was gonna take too long since the store was going to close so I went home to restore from my backup in iTunes. My computer would make a sound after connecting the phone, and sometimes it would show in the File Explorer. But it almost always refused to show the phone in iTunes. I say "almost" because there was a brief moment while troubleshooting with Apple support where it actually showed the "Welcome to your new iPhone" screen in iTunes, but I'm not sure why. That screen was only up for about a second before just going away and showing regular iTunes with no sign of seeing my phone.
I ended up running through even more troubleshooting once live chat transferred me to a call, but my contact wasn't much help either. He basically just ran me through all the steps he had listed on his end before saying he would try to look into it more and call me back on Tuesday. Luckily, the store I got my phone from was holding my old one until I could confirm my data had transferred before wiping it. So I went back there earlier today to transfer the data from my old phone directly. It took about an hour.
So I was trying to figure out the issue tonight since nothing was really solved. What if I want to back up my phone? Why can't iTunes see it? We tried reinstalling iTunes (after moving the folder with my iPhone backup), restarting the PC AND the phone, making sure iTunes was up to date, and I tried other USB ports including the one USB-C port on my PC using the new lightning to USB-C cable that came with the phone. None of it worked.
But just now, I tried one of the other USB-A ports on the computer (the one directly under the Wifi antennas on my motherboard), and now iTunes is seeing the phone. Looking into it, I think this is a USB 3.1 port which confuses me because it shouldn't be the only one. So I'm not sure why only this one works. My phone is getting backed up as we speak, but this definitely sounds like something that's either gonna need a software fix in iTunes and/or iOS OR there's some hardware fault with the new iPhones that causes this to happen, in which case the phones should be recalled and replaced at no charge.
I'm really hoping the right people at Apple get on this because- while I'm glad to see it's not just me- this means there's a real problem here.