I'm a secondary English teacher - I'd never set H/W that absolutely demanded access to a computer.
If I set homework, then it's often to inform a subsequent piece of work (research on the text we're studying, or practising a skill, eg. using connectives, because it'll be a key assessment focus for the completed task).
If it's research, I always ensure it's something they could do in the school library. If it's practising a skill, it's done in exercise books.
Or it'll be the final draft of an assessed, 'portfolio' piece of work - in which case I would prefer it to be typed. & the vast majority of my students choose to do so - they like the idea that they have worked hard on a draft in their books, & now they're submitting a finished, polished assignment in a 'grown up' way.
However, I always make it explicit that handwritten final drafts are just as acceptable - the fact that I find typescript quicker to mark isn't the student's problem!
But whilst I agree with you, CertainAge, that teachers shouldn't object to handwritten work, I'm with janeite on the levels.
Levels aren't 'lazy'. They tell students exactly what they need to do to progress. By the time I've APP'd a student's work, given written feedback, & got the student to evaluate the strengths & weaknesses of their own work - & possibly their peers - well, it's quite a bit more constructive than a mark out of 10.
I've been teaching for 10 years & there's not much in the way of new initiatives that I get wildly enthusiastic about! But APP is very, very effective, & IME it gives students a far clearer & more precise picture than generalised comment alone. Which, actually, they are very positive about.
3littlefrogs - you shouldn't feel you have to provide a PC for year 7 homework! At least, don't rush to get a printer if you're getting a laptop & not a PC package - dd might be able to print off work at school from a memory stick - worth checking.