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Better notation will improve the ability of mathematicians to do advanced work within calculus.

Crap! Smart ass just made a PANTSLOAD of more work for calc students.

It’s well known that Newton invented Calculus, less well known that Liebnitz independently invented Calculus simultaneously, and that who you credited for its invention was a political issue. Brits said Newton, Germans said Liebnitz.
Even less well known is that (as a student, IIRC) Charles Babbage rebelled against the teaching of calculus using Newtonian notation. He demanded - and was able to get - calculus to be taught using Liebnitz’s notation. Since he was in Britain, you can see that he was cutting against the political grain. But his point was precisely that good notation makes learning/understanding easier. And learning Calculus well via Newtonian notation was harder than it needed to be.

I just scanned the paper, and of course, there is no "longstanding flaw" in elementary calculus. . . . I'm not saying it's not interesting, and maybe even useful, but they haven't found a "flaw" in calculus.

. . . The authors come up with a notation for second (and higher) derivatives that allows elementary calculus formulas to be manipulated in a straightforward way . . . This new notation may even find its way into high school and college calculus courses. - thesharkboy

Agreed.