You also do an unfair comparison here - you are OK with portable batteries providing only fridge & WiFi for a couple hours, but expect whole-hole batteries to last a week. Many people use whole-home batteries to bridge typical outages that last <24 hours, and do so without ever having to notice any change of use of their home - powering their full heating/cooling etc.
Batteries and generators are also not mutually exclusive. You can install a solar+battery system because it makes economic sense and pays for itself while providing zero-downtime backup for most outages, while also backing that up with a generator for longer term edge case outages eg long extended outages during the winter or where there is an unusually long “solar drought” - it really depends on how much resilience you are designing for.