FTP is broken regardless of NAT. It flat out does not work with a default deny firewall policy.
Simple packet-filtering firewalls invented in 1988.
In addition you can force passive mode and confine FTP to a range of ports on just about every server and client out there. So your statement that FTP "flat out does not work" is untrue, unless you mean that your firewall is so much default-deny that you cannot even open incoming ports.
However, while it makes me a bit sad, I have to agree that there are better, simpler and more secure protocols now for downloading files. HTTP/2 in particular.
I'm surprised to see WebDAV mentioned here, to be honest, I thought it was a dead horse everywhere except in enterprise.
The modern web is much more about routes, resources, and URLs than directories and files.
FTP is a pretty conceited protocol, and one that deserves to go away. People say it made more sense in the 80's, but I was there and even then *NIX/Solaris admins found FTP to be about as much fun as that IRC pingback identd service; which is to say not very fun.