I have very limited experience with “the button” but I thought I’d give my thoughts based on my current parent situation and what I’ve considered. My dad passed in November and I worry about my stepmother being alone. She had a heart attack about six years ago and if Dad hadn’t been there I don’t think she would have been able to summon 911 herself. She took a spill on the way out of the hospital and while it wasn’t bad I worry that a bad fall is in her future. She will be 68 next week and I’m considering asking my sibs to go in on an Apple Watch 4 for her for the following reasons:
My grandma (82-84) had “the button” and she hated, hated, I mean LOATHED it. She wore it unwillingly. If she accidentally pressed the button it would make he mad that she had to get up to answer the phone to tell them there was no problem. You couldn’t get through to her that she did not have to keep the phone on the charger 24/7. IME people of a certain age do not feel they need their phones nearby at all times like the vast majority of younger folks do. At my parents house their cell and cordless phones were/are always on the chargers AWAY from them.
In the end “the button” failed. We are not sure if the system did not work or if my grandmother did not/could not press the button. This was 16 years ago so I would assume there are much better systems now.
My stepmother would tell me to go to hell if I suggested a button.

She loves her phone though (when she fell that was her first concern) and I think I could get her wear an AW.
Pros for my situation:
I think she’d wear it. Unlike her phone the watch would always be with her.
One time purchase, no fees. (She rarely goes out and when she does she has her phone so wouldn’t need the cellular version)
It will monitor her heart and alert her to possible problems. She could get ahead of the situation.
If she falls the watch will ask if she needs help. If she doesn’t respond it will call emergency services AND me.
You can set up SOS that she can hold down the side button to call emergency services and again ME.
You can make phone calls so again, if she’s in a situation she can call me without her phone that’s on the charger in the kitchen.
It can be worn in the shower.
Cons:
Must have a working iPhone to use it.
They have to wear it at all times. It’s useless if it’s not on their wrist.
Needs to be charged daily. Could be a problem for older people with memory issues.
Not suited for folks who may struggle with tech or cognitive issues.
I’d have to set up and maintain.
Could fail but as mentioned above so can a button.
I don’t know if any of that helps but I can tell you I’ve read about quite a few people who have bought their parents in the mid 60s to 70s age range an AW who are happy to wear them. I think it gives them more a sense of freedom and doesn’t make them feel “elderly.”