For an elderly woman with poor eyesight, a fixed location landline that never needs updating or maintenance is probably preferred over an easily lost phone that needs to get plugged in, updated, etc.
I pay ~$0.50/day for the peace of mind that I can call the police from any major room in my house, whether or not my cell phone is near me, or even has a charged battery for that matter. Also, that emergency services would immediately know my address when calling from my landline, so I could do as little as just call and hang up to get them there in an emergency. There are many benefits to maintaining a landline, and (cheap) cost is one of them.
You know you can cancel your phone service and still call 911 in many states (including the most populous ones)?
But yeah, in this case, there are big-button landline phones with speed dial.
In this particular case, we've tried a big button phone. The problems with it are two fold: first, cataracts impact her straight forward vision and she's not able to remember button placement. Second, it's not uncommon for her to forget what she intended to do before getting there. The simple act of walking to the phone to initiate a call is enough time for her to forget who she wanted to call in the first place. At least in this case, she can act on the thought immediately and be reminded when she gets to the ringing phone.
[^1]: full disclosure: I can toggle my lights with my Echo. I use z-wave light switches though so people that aren't nerds like me don't have to personify the appliances in my apartment.