I totally agree with everything you say and feel about the use of iPads in education. Just to clarify though, it's the Baseline assessment which is done on an iPad at the start of Reception. The phonics screening takes place at the end of Year 1, and is not on an iPad (yet!). Reception teachers absolutely hate this pointless Government Reception Baseline Assessment, which has to be carried out 1-1 with up to 30 children, taking hours out of our precious time bonding with the children in provision during their first few weeks of school. That's where we use to Baseline in the old fashioned way, through observing the children while we play with them all to establish what each one can and can't do when they start school. Now we have this stupid test on an iPad, where children can hit buttons to get in some lucky guesses. Whoever designed it has never worked in Early Years, that's for sure!
As you say, there was a big push on the use of iPads 10 years or so ago. We had them out several times a week, with a timer for each child to have a 10 minute turn on educational apps. Now I avoid them like the plague as nearly all the children have one at home now and most of them show signs of addiction. They don't need to have additional iPad time in school.
As a teacher, I'm highly against setting homework on iPads in Reception. I think there's a place for it when they're a bit older (TT Rockstars, Spelling Shed etc) but not at 4. However, I wouldn't hold it against teachers who do set it as you'll probably find it's their school's policy and they have no choice but to set it.
Schools should not enforce these type of homeworks though, as not all families have the technology or agree with too much screen time. I wouldn't ask for worksheet homework as a substitute though OP, as that's making more work for the teacher (and worksheets are as pointless as apps). Just have a chat with the teacher to explain why you won't be using that app for homework and ask what they suggest you do instead to help. They'll be able to give you ideas of games and activities you can do together which will be worthwhile for your child and not onerous on them to set each week.