I buy iPhones on the upgrade program which requires Apple Care + - $199 for two years. On the non-damage repair part it doesn't really do much the first year, but extends the warranty for a second year (if you keep the phone).
It does cover 2 episodes of damage. For an extra $50 or so a year you can get protection against theft/loss. Last year, the phone I bought was $1250. This year's phone is $1000.
Repairing the screen for $29 instead of $229 is definitely preferable. Basically if I keep the phone for 1 year and replace the screen once I am out $129 as opposed to $229. Of course, I don't always have to replace a screen (I have replaced two in the past). But, the big ticket item is if you have other damage, particularly to the glass on the back of the phone. That costs $550 to replace! It is $99 with Apple Care +.
As for loss and theft, my son lost an iPhone X last year. Yes, I know that is fairly rare nowadays but it happened. And he just had to keep paying for it as he bought it before you had coverage for phone loss. He now has coverage for phone loss on his new phone.
I sprang for the extra $50 a year when I get my last phone. $1250 is a lot of money. I guess I could self insure but this was a situation where I just felt it made sense at least for the more expensive, newer phones. I would pay for it on an older phone.
But, it is a close call for sure.
