You already know how Signal is going to come out here, because this is something people complain incessantly about (the inconvenience of not getting transcripts when enrolling new devices).
It's a bit unfortunate there isn't a mechanism to establish a key between your desktop and smart phone client that would allow message history to be synced over an E2EE connection. It's doable, but perhaps it's an intentional safety feature one can't export the messages too easily.
I agree with the principle here wholeheartedly. One addendum though is I think this isn't quite the same as the mud puddle test. The idea behind the mud puddle test is if you've forgotten everything, but then manage to recover your data, then the principle must be that someone other than you has to have had access. With Signal, they intentionally refuse to sync data as an extra security step even if you have the keys, the software just refuses to do the syncing step. I'm glad they do personally and I'm not contradicting your point, just adding some notes. Just thought it worth noting.
This isn't fully accurate. You can backup your Signal messages on Android with an encrypted file and a key you control. So yes, just installing on a new device isn't going to give you history. I'd prefer they offer a universal structure for that backup file so we could easily switch between Android and iOS and have some way to backup your data at all on iOS (presently if anything goes wrong when setting up a new phone you lose your entire message history).