Their stance is that you personally are banned for life from subs regardless of which account. Would be a real shame if your IP got changed between accounts, your cookies and local storage got cleared, and you never mentioned the old account again. You could accidentally post in a sub you got banned from, and they wouldn’t be able to helpfully re-ban you from the sub!
If you were still trying to spend time on reddit in the first place at least.
Fast food chains aren’t your friend