I have seen many students struggle with long division (especially the Standard Algorithm but also the Partial Quotients Algorithm). Similarly, I have seen many teachers lament this lack of proficiency. I suggest that it is prudent to conduct a cost-benefit analysis for learning these algorithms for division beyond 1-digit divisors.
If students understand the concept of division and perhaps can do long division with 1 divisor, what is the purpose of teaching long division with a multiple digit divisor (or the partial quotients algorithm).
For a long time square roots were computed using a lengthy algorithm, similar in nature to long division. We don’t teach that any more.
Sharp came out with a scientific calculator in 1978. It had a square root button. No more algorithm.