Over-reliance on the calculators is already a huge issue, and we don't need to make it worse.
No. I suggest focussing on explaining concepts, not drilling sums. And explain them why in ancient times the teacher used to use a cheat sheet because drilling didn't work because science found out our minds are not wired for that.
Besides, from over 7 billion people on Earth, how many need Algebra 2? Please try to be honest and give us here an estimate teacher. In your life Math is important apparently, but in most lives it's not. Teach it to those interested please and don't push it through the throat of those not interested.
The research I've seen suggests that having a bunch of stuff at your finger tips then makes it easier to have the concepts crystallise. Trying to start with just the concepts doesn't work.
So what's needed is both, significant practice to help embed the simple underlying facts, with extensive exploration of the links between the facts to help the concepts emerge, be identified, and then distilled.
To me, it seems that almost everyone goes full extreme: "Must do this", "Must do that", whereas, as in game theory, it seems obvious that a mixed strategy is likely the best option.
"Hardly ever"? So when checking the restaurant bill, the change at the grocery shop, the tax return, a bank investment proposal, the costs of building/renovating a house, the time left for a mortgage, do you always use a calculator?
IMAO the current system of teaching math is ancient and above all deprecated. We should not punish our kids with it. I mean, what's the point of drilling stupid sums if you'll hardly ever need it in your life? I think it is totally stupid and irresponsible if anyone does calculations without a calculator for almost any application, not excluding: store checkout, health care, aviation, etc.. The current educational methods are way pre-computer era, it desperately needs an upgrade.
So why not start teaching kids concepts and let them use the technologies we create to solve problems that our minds are not wired for? Ever seen a teacher without a cheat sheet checking the answers? Guess why? Because their own calculations are too slow and above all not to be trusted! And should I not use a debugger because theoretically we can write proper code without it? Come on..
Please stop teaching our kids deprecated workflows. Teach them the best practice, the best way we know and can do now, because: "As the twig is bent the tree is inclined".