In reply to Blue Straggler:
See the first reply to this question on the official Microsoft community forums:
https://answers.microsoft.com/en-us/mobiledevices/forum/mdlumia-mdapps-mdap...
From a Microsoft forum moderator: "Windows Phone app for Mac is no longer available... We removed the app so we could focus our resources elsewhere." Note that that was posted in December 2015, less than a year after the Lumia 640 was launched. It is any wonder that Microsoft's mobile phone efforts died a death?
(Ignore the comment from Philip Anderson's Mother's Son, by the way - it's garbled nonsense.)
Not sure why you were trying to use iTunes - it's Apple's app for syncing with Apple mobile devices. One doesn't use it to sync with Android devices (thank goodness). There is - as you have discovered - no 'standard' for syncing phones to personal computers. Each phone OS does it in a different way. In Android land, each manufacturer (Sony, Samsung etc) has their own app for syncing to Mac or PC. Google does at least keep the generic Android File Transfer app kind of up to date - they don't pull the app altogether because they need to "focus resources elsewhere", presumably because they know damn well a fair proportion of their users want some kind of 'official' file sync/exchange tool.
I am a little surprised that there wasn't a way to get the SD card on a Windows phone to mount as a drive on the Macbook, like you can do with Android by enabling MSC mode on the phone when you connect it to the computer via USB. As you mentioned, though, it's as easy to do that directly from the computer to the SD card without the phone needing to be involved.
Final point: IME file transfer via Bluetooth is and always has been pretty flaky. It's based on the OBEX protocol which was originally developed for the Palm III (those devices were launched in 1997 and are now, literally, museum pieces - as in, you can see them on display in museums.) According to the Wiki article about OBEX, support of OBEX on Windows Phone 7.8 and 8 devices is: "limited to the transferring of pictures, music and videos via a 'Bluetooth Share' app". Whether that app is still available, and whether it would be better than doing it the hard way like you did, I couldn't say - I've not touched a Windows Phone since 2016, when I configured 300-odd of the things for a major financial institution. That was fun. (And I do sometimes wonder whether anyone got fired for that particular far-sighted decision!)
Post edited at 11:10