While Signal's greatest strength is its privacy features I think that at some point they are going to have to meet their customers/prospects/users' other needs.
The biggest one being the availability of chat history anywhere, anytime at their own risk if needed.
We won't educate people to use messaging app in the way we want them to (for privacy sensible conversations only) because the vast majority don't use messaging app like that.
It's either give up on that idea or heavily advertise that Signal is not a Whatsapp/Telegram/Viber/Messenger/Whatever replacement: it's a tool to use when you want to have private conversations.
Maybe it'd be better to leave the Signal messaging app lives its life and allows a third party chat history viewer to emerge. You can already export your encrypted backup to a readable CSV file. https://github.com/xeals/signal-back edit: which obviously doesn't work with a corrupted database :p. Signal backup as a service startup ?
Point in case: mom complained the other day that Signal Desktop took some time to launch because it was “syncing things”. I told here that this syncing from her phone to the computer is the proof her messages only exist in the application. Desktop or smartphone, that's why it needs to sync, facebook and others don't work like that (I grossly simplified).
note: Thread with comments like is how I remember HN is now a site with a huge audience.