The science must be missing some inputs because the current theory is lacking.
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).
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 had a job 10 years ago doing in-person training at a company trying to digitize their paper-based office for the first time. They were in a commodity distribution business, so while the math isn't hard, there is a lot of day-to-day arithmetic (conversion between unit of measure and price/unit vs total price) for all the employees from the warehouse guy to the sales staff.
The system introduced a change in their workflow. Before in their old manual paper system, people just kind of put things on a truck and figure out later how much got shipped and how much to invoice a customer. The whole can be very hand-wavy. There was no live inventory system either.
Digitization meant that sales have to write sales orders that had precise units to be sold. Based on inventory, they know how much they will actually ship and they know that down to the dollar. Everybody suddenly had to start being aware of the math involved in their work.
It was kind of funny to see a bunch of blue-collar, ex-con, high school dropouts learning faster than all the college-education office workers. The college-educated guys were too drill-orientated and approached the work like the math worksheets that everybody is talking about. The ex-cons had a working relationship with the numbers on the screen and the things that are hanging off their forklifts. Many of the white-collar clerks had been getting by memorizing formulas. They had no idea what any of those formulas mean.
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.