Yep. See the perennial complaint about Signal as a demonstration of that. They don't persist your messages across devices on privacy/security grounds. That's fine, it's why I use it (or one motivation for me to use it). But it's contrary to what many people expect from that kind of service.
Full E2E encryption is going to trigger nightmare "I lost all my photos" customer-service stories when people forget their passwords... which is acceptable when you deliberately signed up for a service where security was the selling point, but not great for someone who bought a mass-market phone.