Clearly every point in the chain matters, but it always surprised me that a company that puts so much emphasis on security and privacy thinks it's a good idea to keep your messages in the cloud:
"Unlike WhatsApp, Telegram is cloud-based and heavily encrypted. As a result, you can access your messages from several devices at once"[1]
Unfortunately, it sounds like that's not what Telegram is doing with its non-"secret" messages.
Of course, whatsapp could register devices which are thrown away after x days without delivery then store the messages until delivered to all end devices but that's likely a core infrastructure update which would require them to store more data, not the same as just writing another client.
Still, what they've created as a web client is a little batty; typically I'd want to use those when I can't find my phone.