I agree with you. My mother is 67 years old. She was familiar with Macs when she got an iPhone 4 three years ago. She liked the small size of the phone because it fits nicely in her hand and in her pocket. She does use reading glasses so I increased the size of the text which is very helpful for her especially in Messages. It took her a while to get used to texting on a QWERTY touchscreen since she was a two-handed pro on a flip phone. She’s gotten used to having the power of the Internet in her pocket. She likes being able to look up stuff like addresses, phone numbers, crossword puzzle answers, the latest lottery numbers, etc. She likes the Facebook app to keep up with all our relatives and her banking app to keep track of her finances. She also likes having a good-quality camera on her at all times to take pictures of her grandchildren. As far as storage goes, she has very few apps so the majority of the 16 GBs goes to storing photos and videos. She filled it up once with photos and videos but I transferred them to her Mac and recovered a lot of her storage space.
Last year, she inherited my sister’s old iPhone 5. And while it would have been a perfectly fine replacement for her for a year or two, the digitizer unfortunately started acting up really bad this past February. The screen would quit responding or start ghost typing so I told her to stick it out until March 21st when Apple was set to unveil the new smaller iPhone. I watched the event and knew instantly that it was the new phone for her for all the same reasons you stated. So on March 31st, I went with her to our local Verizon store and upgraded her to a 16GB Rose Gold iPhone SE. She got a nice, clear, soft-grip case to show off the Rose Gold color and a tempered glass cover to protect the screen. So now she has a iPhone that could potentially last her for the next 3-4 years assuming it doesn’t break down internally or slow down to a crawl with a new iOS update. If anything, it might need a battery replacement in 2-3 years. (I had an iPhone 3G for 3 years and a 4S for four years. They all lasted. I only had to upgrade the batteries once on each model. So it’s possible.)
I hope this helps. Let us know what your Mom decides.