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:
Avoiding an identifier tied to your identity, hiding identity from governments or people who know your number.
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.
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I wasn’t so much trying to solve anything as much as I was trying to compromise and meet the devs halfway on the issue of spam account creations.