<..> What is it really impossible to write posts from a new account? <...>
According to the forum rules, banned user is not allowed to write posts except appeal topic in Meta, until the ban will be lifted.
25. Ban evasion (using or creating accounts while one of your accounts is banned) is not allowed. ~
If you get banned (temporarily or permanently) and create a new account to continue posting / sending PMs, it's considered ban evasion. The only exception is creating a thread in Meta about your ban.