A couple of things.
Just in case anyone actually wants to know why Apple might not want to say that they were the authors of the standard, even if they were. This is sheerest speculation, of course, but it's pretty obvious stuff. All you need to do is look at what happens when Apple authors a standard.
For example, Firewire. Which is also known as IEEE 1394, a, you guessed it, standard. For a while Apple wanted a licensing fee to use the NAME, but otherwise the whole thing was free. And eventually they dropped even that. But a number of industry groups (at the time led by Intel, but also including quite a few other household names) did their best to ensure that it would never be widespread, instead creating and then adopting USB-2, which is wholly inferior to firewire. USB-2, admittedly, was designed simply to be cheap rather than good, but if Firewire devices were ever made in anywhere near the numbers that USB-2 devices were it would have driven the cost of controllers down to a competitive level. But a consortium of companies simply did not want to adopt anything with the 'Apple' name on it.
Now, Apple in 1994 was in a rather different place than they are today. Still, if Apple had come out with a spec, waved it around, and said, "We want this to be adopted as USB-C", there would have been a lot of companies that would have fought that. There are plenty of companies who, if given the chance to give Apple a black eye without costing themselves a dime, will take it. And tying up a standard in a standards body is more or less no-effort. You just need one person to throw some sand in the gears, and you might as well just give up. (This is, at least, true of the standards bodies that I have interacted with, on a pair of RFCs.)
Incidentally, there are also a lot of people on various standards bodies who are GNU diehards. No idea if this one contains any, but a lot of those people would sooner go back to USB 1.1 than adopt an Apple-authored standard, even if it is completely free of all encumbrances.
Second, in case it isn't obvious why they didn't use Lightning: first off, it's too slow. Second off, it doesn't carry enough power. Third off, it can't transmit multiple video channels. Fourth off, you cannot imagine what would happen if you connected both audio in/out and a hard drive over a single lightning connector, not only due to bandwidth but because it doesn't support isochronous-mode communications/dedicated channels.
Third, in case it isn't obvious why they didn't make it mag-safe: two reasons. First, they would have to open magsafe to everyone if they made usb-c mag-safe. They MIGHT be able to include a licensing deal that let people license it for free only for the purposes of making USB-C connectors, that would depend on the rules of the standards body (which I don't know). But then it would be utterly obvious that it was an Apple technology, and, well, see above. Second, though, has already been covered. Some people are utterly perfect in their ability to keep their laptop firmly on their desks, not jog cables, not in short do anything that could in any way break their connection. They don't NEED magsafe. Those of us who do occasionally catch the cable on something, even if it's sitting on our desks, are fine with accidentally disconnecting the power cable. Accidentally disconnecting the power, the external hard drive, the monitor, the ethernet, the keyboard, the mouse, the connection to the remote server that you're copying data from onto the external hard drive, or even the external hard drive THAT YOU BOOTED FROM, is not so trivial.
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