Well, you can set up Dynamic DNS or (my favorite method) set up a persistent reverse SSH tunnel from the NAT-ed client to a world-facing server.

You're welcome to walk my mother through this process.

What would a venn diagram look like between people like your mother and people that want home automation? My mother is still firmly in the "why would I want an automatic garage door?" category.

I think something like an automatic garage door opener is a reasonable thing for someone to want; same with, for example, a smart HVAC system or potentially security cameras.

It obviously drops off sharply when you start getting into the Bill Gates territory where monitors on the walls adjust their artwork to suit the people currently occupying the room, or modifying the light levels, etc. But all the previously mentioned stuff seems like a reasonable thing to want, the same as an automated washing machine or a microwave oven became standard items.