This was one the signature things Steve Jobs spoke of on that first iPhone presentation , 2007 wasn't it. The swipe to unlock feature so touches and pokes in pocket or purse could not turn phone on accidentally. He specifically mentions it.
The OP specifically asked for not receiving the, "use Samsung" or "jailbreak" answers. But I see so many can't read. So looks like the two best answers are:
1. Use Apple Fingerprint ID. Since there have been numerous complaints on here how the fingerprint ID is so fast on the 6s Plus that it is now
TOO fast for some. This seems to be the one button solution the OP is looking for. I can verify that the fingerprint ID is so fast you
can't not turn on the phone from sleep with just one touch. Plus if she hasn't been using security, she gat that added feature thrown in.
2. The other option that would work is turn never sleep on, leaving screen always on and thereby only needing to touch the answer button when she gets a call. Lousy battery life, and potential for answering while in purse or pocket and zero security, but it gets her the most important thing, one touch answer.
Since the OP didn't exclude this answer, going to a flip phone would also work for her. As simply flipping it open would answer the caller. Plus she could be the envy of her friends as being only one with the special flip phone. Who knows, might even bring the popularity of those phone back.
So, OP have you tried these yet? Does any of these solutions solve your "infuriating" problem on your $850 premium state of the art phone? We are waiting to hear if life is again worth living, or did you find another solution like cutting your nails to get better swiping accuracy.
If time saving is your goal, get an Apple watch. Makes a lot of things easier/faster.
Don't think this will work. Time consuming raising arm. Plus with long nails it's ever so hard to put phone on with that pesky strap to fasten.
Slide to unlock is an integral part of iOS. There is no disabling it - stock.
There are however, jailbreak tweaks that can remove it. But 9.1 does not have a jailbreak yet.
Did you not see she doesn't want jailbreak. Stop pushing jailbreaks.