The science must be missing some inputs because the current theory is lacking.
I don't have an opinion on the issue at hand. "Because the science says" With nothing in support makes me really suspicious. It really starts looking like "Because $authority says so you may not question" Which is the opposite of what scientific inquiry is meant to be.
They can still remember some peoms verbatim over 70 years later (in my grandfathers case). And they still remember/understand pretty much all the math they were taught. When I was doing my Advanced Highers (final exams in Scotland) I was asking my parents for help and they could answer all the questions without looking things up.
I looked up the exam paper[0] I sat, I'm pretty sure there's no way I'd get an A again if I sat it right now without studying for it. But I'm pretty sure my parents still woudl.
[0] https://www.advancedhighermaths.co.uk/wp-content/uploads/201...
I am not telling you to do multiplying digit only 1 times. That would be silly. I would be telling you should mix up multiplying digits with other previously learned concepts, say 10 addition and 10 subtraction questions, and the rest can be 80 multiplying digit problems. I don't know the optimal intermixing ratio here, but it shouldn't be a straight 100 multiplying digit problems which all use the same algorithm to solve it.
Drilling and repetition is good, but there's the danger of having illusory mastery because it's already there in short term memory. Your goal is to encode those skills into long term memory.
IIRC (see the above, it applies to random comments on the internet) drill work is more effective (but feels less effective to both teachers and students) if it's mixed up with different topics or question types, kind of like how doing a kata is better than doing exactly the same punch 10x (obviously katas are not ideal either, at least not as the only tool).
Really you need a bit of diversity, and IMO two of the big traps to fall into are overly homogenous drill work (which doesn't retain as well as mixed drills, but looks effective because anyone who doesn't eat their crayons can do it without thinking too hard) and one-off problems (do an assignment where you solve a heavily obfuscated problem once, then pretend that it's now something that students actually understand, when they've literally just answered one single question assuming they even did it themselves).
