I live with my 97-year-old mother in order to take care of her.
She walks with a walker.
She refuses to have strangers in the house who could take over for me when I step out (in case of emergency).
Both incoming calls and outgoing calls (other than 911) are problematic, so I want a phone that offers neither of those things.
That takes care of your answer but...
If she can not press an emergency button on a phone or on a necklace or bracelet maybe she should not be left alone.
Get a caregiver that can come in 1 or 2 days a week. That way you can get away when it is not an "emergency"
Introduce the caregiver to mom as a "friend" of yours.
"Mom this is my friend Betty. We are just going to chat a bit then I will get the laundry done"
You and Betty talk about the help that mom needs and Betty gets up to "help" you do laundry.
Later you can say "Mom, Betty, I forgot to get milk I have to run out will you two be ok for a bit?"
Then leave for an hour.
Mom will get used to Betty and and Betty can help mom by getting a drink or just chatting while Betty folds the laundry.
A day or two of this and mom will get used to Betty.
A. You never leave the house.
B. Mother stays home alone at times.
C. You take Mother with you everywhere.
D. Someone else supervises Mother when you go out.
It is hard when someone is dependant on you.
A. Is not practical or preferred (unless you love being a hermit).
B. Risk. How long is ok alone? Is she a frequent faller? Would she try to go outside? Cook? Do risky stuff?
C. Picturing running around during 6 errands in one morning.. Now please do keep up Mother.. Nope.
D. Less spontanious. Need to be pre-booked. Finding the right person may take a while. May even need a trick or fiblet. But don't write off option D. due to a senior tantrum of Mother saying no. It's for BOTH of you anyway.
For her safety + your peace of mind.
My folks have a regular afternoon a week sitter. Everyone knows the routine. *Someone* still tries to cancel every other week.. because they say they 'don't like it'.
They get anxious with sitters.. too bad. They fell when left alone. They lack insight about he situaion & are being a senior brat. The adult in charge needs to be reponsible & make the arrangements they need to.
If your Mom "...simply doesn't have the mental wherewithal to hit a button in an emergency" she very likely won't remember to call 911 on a landline that she doesn't use on a daily basis. My 95-yr old Mom is recently forgetting how to use kitchen appliances that she's used every day for decades. A phone is no different.
Also, what type of emergency are you imagining? Her most likely emergency would be a medical one, like If she falls -- she likely wouldn't be able to reach the phone anyway. Would she even remember her address to tell EMS?
At her advanced age and history of resisting adopting to new things, I don't think there's going to be a clean solution for her situation because a lot depends on her ability to learn and retain a new thing.
Will she know to call 911 in an emergency? And will she know how?
If this is your desire, you can turn the ringer volume off on a typical landline phone.
At least when I last had one. Then, No Incoming Calls.
Is it a problem to be able to make outgoing calls?
You might consider investing in a "Life Alert" type pendant, or device which sits on a counter which only makes emergency calls. But there is a monthly cost, because the calls get routed to the company's call center, then directed to the appropriate responder.
Another option would be to install a camera in the house so you can look in on her when you step out. It will also allow you to talk to her, which would be nice, with no phone for incoming and outgoing calls.