To send a file from one computer to the other by internet (although often internet should not be needed for this), I think netcat should do. Use tar or something else like that if you want to send multiple files. Use programs to calculate the hash if you want to verify the hash of the file. For large files, it does help to make resumable transfer; fortunately, that can be done easily, too (you can see what the file size is and use the "tail" program to skip some).
You should not need HTTP, FTP, etc. You should be able to use something which can work on any computers, such as just TCP/IP. Unfortunately, some systems (especially some Windows systems) will make that difficult. Using the more complicated such as Magic Wormhole and other programs means you will need two computers that support such a thing. I did once try to transfer a file from Windows to Linux, and had to install ncat to do so but Windows deletes it by default if you try to do that, but I was able to make it to not to do that.
How do you transfer between computers behind NAT or firewalls without an intermediary?
If you have to install software anyway why not install wormhole directly?
Netcat works in some circumstances and it’s fine to use it in those. But wormhole covers different scenarios and your netcat proposal doesn’t cover or have advantages in some of them.
It is unfortunate that you would have to install netcat on Windows (I don't know why they don't include functions such as that built-in, perhaps it could be included as a function in PowerShell); but on some other systems it is likely to already be installed, and such a thing really ought to be included by default if the computer has TCP/IP included by default. This does not necessarily need to be netcat; it can be any program that does the same thing, and it is simple enough to include with TCP/IP based systems that other kinds of operating systems could potentially have their own variant, if they have the ability to connect to the internet.
However, it is true about considering NAT. Then you will need to set up the intermediary (which further affects compatibility), if you cannot connect the computers directly (which also ought to be possible with a null modem cable, but that also is often not available).
It also does not consider multiple files at once; how that should need to be handled will be different on different computers anyways though, since the files are different on a different computers.
Due to such things, other programs such as Magic Wormhole might help, although even then it will not necessarily work with all computers anyways, because then you will need a computer that is compatible with Magic Wormhole.
Another alternative, that might sometimes be suitable, would be LAN connections. This is not always suitable, but if they are, then you can use the LAN addressing directly, too.
You should not need HTTP, FTP, etc. You should be able to use something which can work on any computers, such as just TCP/IP. Unfortunately, some systems (especially some Windows systems) will make that difficult. Using the more complicated such as Magic Wormhole and other programs means you will need two computers that support such a thing. I did once try to transfer a file from Windows to Linux, and had to install ncat to do so but Windows deletes it by default if you try to do that, but I was able to make it to not to do that.