I've seen this explanation multiple times through the years, but as I said it's entirely possible it was just a post-hoc thing somebody came up with. But as you said, it's fun to argue/think about, so here's some more. I'm talking about the ASR-33 because they're the archetypal printing terminal in my mind.

If you look at the schematics for an ASR-33, there's just 2 transistors in the whole thing (https://drive.google.com/file/d/1acB3nhXU1Bb7YhQZcCb5jBA8cer...). Even the serial decoding is done electromechanically (per https://www.pdp8online.com/asr33/asr33.shtml), and the only "flow control" was that if you sent XON, the teletype would start the paper tape reader -- there was no way, as far as I can tell, for the teletype to ask the sender to pause while it processes a CR.

These things ran at 110 baud. If you can't do flow control, your only option if CR takes more than 1/10th of a second is to buffer... but if you can't do flow control, and the computer continues to send you stuff at 110 baud, you can't get that buffer emptied until the computer stops sending, so each subsequent CR will fill your buffer just a little bit more until you're screwed. You need the character following CR (which presumably takes about 2/10ths of a second) to be a non-printing character... so splitting out LF as its own thing gives you that and allows for the occasional case where doing a linefeed without a carriage return is desirable.

Curious Marc (https://www.curiousmarc.com/mechanical/teletype-asr-33) built a current loop adapter for his ASR-33, and you'll note that one of the features is "Pin #32: Send extra NUL character after CR (helps to not loose first char of new line)" -- so I'd guess that on his old and probably worn-out machine, even sending LR after CR doesn't buy enough time and the next character sometimes gets "lost" unless you send a filler NUL.

Now, I haven't really used serial communications in anger for over a decade, and I've never used a printing terminal, so somebody with actual experience is welcome to come in and tell me I'm wrong.

What's up with all those equals signs anyway?