Could someone not build the case you mention (shock, spill proof, easy hold) with a big speaker in it?
Not sure if you know this, but the latest iPhone SE still uses the iPhone 8 body complete with home button. Depending on which phone he's on, it might be a good idea to upgrade; all of the rumors that I've heard are that Apple will make the next SE on a different body.
Changing to the newer iOS was challenging for her due to the significantly smaller and pushed to the top call answering buttons. Apple does a lot for accessibility, but I really wish they had an “old persons mode”.
In the meantime, you should be able to solve the call banner issue through a relatively hidden setting; Settings > Phone > Incoming Calls > "Full Screen" should put things back to the way they were.
[0] https://www.apple.com/newsroom/2023/05/apple-previews-live-s...
I really dislike the little banner thing and much prefer a full-screen image of whoever's calling.
I know because one of my previous iPod Touch devices had a broken physical home button so I used the assistive mode sofware button instead.
This might also work for people who are too old to understand how to use the phone without the physical button.
I kept a PC working for my Dad the hard way for years. Luckily when his previous email client became unworkable and confusing we managed to switch him to google mail (which I could more easily help with remotely) and he could be talked through the TeamViewer settings. He carried on using that for several years, delighted to be able to email people, until his interest in using the PC began to drift as he got to 90, mostly I think because it became more difficult for him to read (it is amazing how much the eye's transmission of/sensitivity to light changing over time makes interfaces more difficult or can even make them seem "new", and that is when the interfaces were not changing or doing unpredictable things).
But we never managed to really get him to use a mobile phone. He could do that only fitfully despite some great device designs, and he would reject them quickly. He would forget to charge them, lose the chargers etc., and sometimes would confuse charge and signal strength, or assume he had to switch off the phone to save money.
He would likely know how to use a mobile in an emergency, but of course the day he first wandered off and completely disappeared for hours, he didn't think that was an emergency at all!
As another poster says, I would take this opportunity to upgrade to the last SE with a button while you can. There's a very good chance his muscle-memory skills will translate just fine, but I suspect you are right about swiping up.
FWIW I think swipes starting "beyond the screen", as the Palm guys used to say, is a bad design. I think the number of top-down swipes in iPadOS is confusing and annoying, and I'm not that much more than half the age my dad reached.
I wish you the best in continuing to support this sort of stuff for as long as your father needs it -- keeping someone able to use technology is not just a "nice to have", it's a connection to the modern world that means a lot.