That's what I would have suggested. iTunes is not dead. It is still the Apple media player for the current operating system version. Even when Catalina is released everything will likely be very similar, just split up and renamed. If they rename a bridge does it stop working? Right now, connecting to iTunes is the major alternative to doing a wifi update and the only one if the wifi update is not working. Whether or not you choose to try it is up to you.
Here's your alternatives:
Update your iPhone, iPad, or iPod touch - https://support.apple.com/HT204204
Even if you take it to Apple, it is what they will try first.