We get tons of posts from users asking about bans, perhaps assuming that their case is somehow different from the others, or that the ban was incorrect, or that they need to ask a question now, etc. Of course, the intent of the ban is to get those who just want to post crap to leave the site, and to get users who genuinely want to learn the guidelines to know the only way out of a ban is to improve their existing posts and have them upvoted. Also, for question bans, users are given the opportunity to ask one new question six months after the ban.
The wording of the ban message, "we're no longer accepting new [questions/answers] from this account", is very contradictory to the above, and seems to encourage people to bypass the block. Let me break it down for you:
We're no longer accepting new [posts]
This wording, by itself, implies that the decision is final, irrevocable, and will not be considered further, which directly contradicts the truth. We are willing to reconsider after they have improved their posts so they're well-received. (But not otherwise, but it still contradicts the truth.)
from this account.
This part, especially the word "account", encourages users to create new accounts and change their IP addresses to keep posting their crap. As the anonymous editor, I was susceptible to getting my IP banned just for submitting one edit that tripped a filter, and I used a VPN to successfully bypass those blocks. I imagine that the post ban IP filter is probably that easy to bypass as well.
Anyway, to summarize, that text implies that the block is final, and the only way to get past it is to create another account. We don't want those users to keep posting crap after having been warned and rate-limited; we just want them to either just leave or learn how to make good posts. For this reason, I think the ban message should be reworded. I'm not quite sure what it should be, but here's one suggestion:
Your ability to [ask/answer] questions has been revoked. For more info, see [help].
That refers to "you" as a person, not a specific account.
If the message can be longer, here's another suggestion:
Your ability to [ask/answer] questions has been revoked, because your past posts were not received well by the community. You must improve those posts before you can post again. For more info, see [help].
Let me cite some example users who recently posted about their bans here on MSE: one user came out to us that they had used 30+ different accounts to keep posting crap after getting banned 30+ times. Another user's more recent questions were very well-received, but their past posts were very negatively received, and even after posting good questions once every six-month allotment a few times, were unable to get out of the ban. Thus, I think it's important that our ban message refers to "you" as a person, not a specific account, and includes instructions on how to get out of it (if they're willing to follow them, of course).