You currently need a phone number to sign up for Telegram. Add an option to sign up using an email address or another method, like some messengers do (e.g., Wire, Matrix, Threema, Session).
Potential spam issues could be mitigated by:
Only allowing addresses from major email providers at first and slowly expanding reach if it's manageable.
Automatically limiting such accounts from contacting strangers until their perform some additional actions.
Allowing group admins to prevent such accounts from posting by default.
Use Cases
Avoiding an identifier tied to your identity, hiding identity from governments or people who know your number.
Workaround
Use a virtual phone number.
Warning: Do NOT use temporary numbers to connect to your account, as you may lose access to your account when you lose access to the number.
So in my country you can buy them on eBay. Normally in my country you have to show your national ID card or something to buy a Sim card or more clearly, to activate it. These are pre-activated by others, the names on them are quite suspicious, seems like fake IDs are being used to verify them. But why would you care, as long as it isn’t registered on your name. By law you can buy activated Sim cards but you should do a ownership transfer. But really no one is checking who currently owns the Sim card so if you just do not do the ownership transfer you can use a Sim card on someone else’s name basically you’re anonymous then.
But I live in one of the most free countries in the world so… I feel there are places where this would be much more difficult or at least could get you some serious trouble.
Brandon
You don’t even need a SIM card. Just download a VoIP app. (most of these are free and give you a northern america number e.g. +1 ___ , if you don’t mind that)
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We need something that is open source or decentralized
In my country you legally need to verify you identity, but that doesen't stop you from buying a pre verified SIM. People sell them, even in bulk.
Given you found a way to purchase it anonymously.