Batteries alone are not suitable for long duration outages, but solar+batteries, designed correctly, can not only supply enough power during long outages, it can get you to be off-grid entirely in the first place at a dramatically more cost effective number than your $500k quoted - perhaps 1/5 or less for a system suitable for your needs of 115kWh per day. So while the system might be more expensive than a generator alone, it can still beat on value because it provides power all year round.

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.