A SPA's network dependency or robustness totally depends on the product's design. Some types of applications lend well to offline first (anything where the user owns their content/data, todo, notes, documents, pictures, etc). Others are much more dependent on fresh data. Which pretty much means anything big enough it's unreasonable to replicate it to the device.
I'm a fan of "offline first" design and have been a proponent at various companies. To the point where I can build the feature in at very little additional cost if it is considered and decided in the design phase. Bolt-ons patterns are messy.
However, the reality is that very few customers see this as a significant advantage. Which means that it doesn't really translate to market success. If budget is the #1 priority I can't in good conscience advocate for offline first unless it's going to offer a significant win for the company somewhere.
There is a Chrome-only local file system API.
Generally SPAs are limited to browser provided storage like IndexedDB.
This has been easy to implement for as long as I can remember, so not sure why'd you say it's terrible. What stopped you previous times?
not everything is equally affected by bad network conditions, SPAs generally are very badly affected by bad network conditions, indeed what is a bad network condition for an SPA might be acceptable for a traditional static page.