So, to reiterate what I said in staff chat myself. Keeping the two seperated is at best pointless and at worst actively harmful to the community. If a person does something that's considered such a flagrant violation of our rules that they get themselves a permanent ban or has been banned so many times they've been permanently banned, clearly that shows they will not be a positive influence on the wiki itself, so I don't see a reason that permanent bans shouldn't be carried over onto the wiki.
The chat is a firmly ingrained part of the community, and you'd be harder pressed finding someone in chat who isn't a part of the community than the other way around. Because of this, I feel not banning people from both the chat and the wiki after a permanent ban allows them to hurt the community twice over.
That said, punishments should not be 1:1. Messing with Helen, as someone didn't realize that rule, shouldn't be carried over to the wiki. Along with the fact that admins have to manually ban a user when punishment is needed, adding chat related bans into that would just make it more frustrating to have to deal with. Basically, punishment between site and chat should be kept separated, at least until the bans start getting into yearlongs or longer.
Because I feel that most of these punishments shouldn't cross over, it would be unfair for evidence from one medium be used as evidence for a ban from the other. I also don't feel that chat and site should be completely integrated, as chat moderation is an entirely different bear with an entirely different toolset. Maybe in the future, chat staff could be made like a team on staff, but I feel it's too disparate for now.
And of course, there are exceptions to everything. I feel permanent bans could use a bit more discussion before they get implemented, due to this fact.
Lastly, I want to adress the final question in the above post.
4. Should any policy change be applied retroactively or only take effect for future incidents?
I'd say yes. I think it'd be unfair to have someone be given essentially a second chance, when others would not be given the same chance in the future. However, so as not to completely blindside them, I feel they should be given the chance to plead their case before the policy is implemented in full.
TL;DR Chat shouldn't be fully integrated into the site, but permanent bans should be.