If those kids were truly applying themselves to the algebra, I think they'd quickly internalize arithmetic too as they used it. But whatever reason led those kids to not do arithmetic without a calculator could well be a reason they don't do well at more advanced math.

My point is failing to learn the basics is a huge hurdle to learning more advanced things. You posit that one could learn the basics and the advanced math at the same time. Maybe, but that would clearly be harder than doing them in order.

Fluency in arithmetic isn't something drilled into kids just to be obnoxious, it's foundational to almost all future math skills.