In addition to the other useful answers... there is a general "problem" that computers, given the long-known algorithms, ironically many not really human-executable, can do almost all of the algorithmic parts of k-12 and undergraduate and some once-upon-a-time-grad-level math. So it seems silly to struggle to teach kids to do things that machines can do better (the superiority of calculators at arithmetic was just the beginning...)
The genuine sociological and pedagogical problem is that humans are not getting smarter or more capable to keep ahead of things that can be implemented algorithmically on machines. And, to add insult to injury, the same kids that had trouble getting the algebra right in by-hand-calculus will typically have similar troubles getting the input right to have software do it.
That is, math software mostly helps the most able people.
Returning to some aspect of the question at hand: yes, it is ostensibly silly to teach algorithms that are far-better executed by machines. (I don't know whether anyone's bothered to write Latin or classical-Greek or classical-Hebrew grammar-checkers...) Ideally, yes, it would be better to use the machinery and allow kids to look at higher-level issues.
However, sadly, those higher-level issues are intellectually more taxing than (pointless, yes) execution of algorithms. I am disappointed to report that my experience with trying such things generates such reports.
That is, the kids who'd make sign errors or not be able to do middle-school algebra will also be flummoxed by trivial computer-language syntax, etc.
Nevertheless, it is better to be honest, to be genuine, to have math courses address real issues rather than traditional-fake. But we must brace ourselves for the disappointment that there'll still be a cadre of kids who can't do it... now for just-slightly-different reasons than the reasons for which they couldn't do hand-executed algorithms.
So, yes, one should not insist on hand-execution of algorithms, but giving that up and doing better things will make it harder, overall, for the students. But that doesn't mean we shouldn't move in that direction. A tough situation, quite seriously, in my opinion.