Eh, like said, I'd be recommending involving as many different ways as possible, as early as possible. Lets you figure out what actually works for a student without forcing some to spend years slamming their head into a wall that isn't going to budge. Guess if I were doing some kind of ideal, resources and time unconsidered, I'd be splitting curriculum up, have part of the time dedicated to using and becoming familiar with a spread of methods (hand, mental, calculator enabled, spreadsheet enabled*, etc.) and the rest let the student choose two or three methods they prefer. Still probably require the use of more than one, but don't hinge most or all of a student's material on a single style, and make sure there's room for them to work and learn in a manner they're comfortable with, instead of assuming things need to be done a certain way for it to be "right".
Seen a number of times over the years where folks were insisting on pure hand written stuff for students it was very obviously massively frustrating for. Not only did they at best no learn well, often enough they didn't learn at all, or found the experience so stressful and fruitless it actively degraded their ability to engage in mathematics. Regardless of whether math needs to be taught like that, if it's not working it's not working, and it's time to try other things until something does. If missing out on some of the underlying concepts is what it takes to avoid turning someone off math entirely, methinks it's time to shove the concepts under the bus and come back later, y'know?
* Which would take a bit of work to get intuitive for younger users, but I'm pretty damn sure it's possible and being able to physically manipulate a formula and change numbers on the fly without getting (as much) human error involved can be bloody tremendously helpful. If I had had that about a decade before I did, it wouldn't have taken that decade to stop being substantially hostile to the field.