My Mom is 72.
She walks 2500km per year, so about 7K per day (just under 5mi for you imperialists).
Running shoes for running last 600k ish.
She's wearing running shoes (Asics GT2000 ) and doesn't think she needs to replace them since the soles aren't worn through. Does she need to replace shoes as often as if she were running? She would hate the thought of new shoes every 3 months.
Well, walking takes more time on feet, so one would think that running shoes would wear out faster if you walk in them. However, one of the key points of having running shoes for running is to absorb the impact forces, which are much-much lower when walking.
I'd say running shoes last at least twice the mileage for walking compared to running, so your mom is fine to replace her shoes every 9-12 months. I'm no expert tho, but even if I was, it still boils down to how the feet are feeling.
I’ve worked in running stores for years, and I’m not sold on shoes only being good for x distance. I think it’s more important to focus on how the foam compacts over time rather than how many miles the shoe has. It depends on how her feet are (preexisting conditions, etc), but realistically I think you could get away with 2-3 pairs if they have a relatively high stack height to account for midsole compression over time.