Telegram doesn't use end-to-end encryption by default. It's marketed as a secure messenger, but it's comparable to Facebook Messenger or Google Allo.
So, if you use Secret chat on mobile and go to desktop, you'll not see it!
Switching back and forth between secret and not secret is troublesome especially when the other side doesn't know if you are on desktop or mobile to check availability for secret chat.
Note that Telegram secret chats are end to end encrypted (default chats are not) but you're still dealing with the Telegram server (not peer to peer)