The marriage between move-comments-to-chat and chat's features is not quite perfect, but like a good marriage it has been slowly improving. Something like this would drastically improve the usability of move-to-chat by better matching expectations. After all, isn't littering Main sites with
let us continue this discussion in chat
… which turns out to be just a dead link, doing a disservice to regular Main-site readers and users? Sure, those could be cleaned up as obsolete, but why not make a small change to chat to make these links follow the principle of least surprise and not be dead links.
It's odd that we would automatically create so many dead links, when dead links are so anathema to SE.
Counter-proposal: Only freeze move-to-chat rooms
Move-comments-to-chat rooms are a distinct category of chat room and shouldn't be treated exactly the same. However, the easier the change, the more likely we'll actually get the feature, right? So instead of changing links and messing with transcripts, why not just not delete the room?
A frozen room can be accessed and read just as easily as a transcript.
(Aside, this would have the bonus of making valuable move-to-chat rooms more likely to stay alive and useful, as a visible but frozen room is easier to for someone to notice & request to be unfrozen by flag, just like regularly happens with more “normal” chat rooms that occasionally get frozen, but are active enough to not be deleted. This improves the viability of move-to-chat rooms, and by extension the practical utility of our moving comments to chat feature.)
Adding an exception to the freeze/delete script to detect and not delete chat rooms that have an associated post would solve this, giving us accessible moved-to-chat rooms. They shouldn't be too hard or processor-intensive to identify: the first message is always a link to the question posted by the “Stack Exchange” bot.
We'd have more rooms littering chat. But then, I don't think we're actually worried about this, since we're OK with frozen rooms littering chat's room lists anyway, and we're already eager to create move-to-chat rooms. Having a few more frozen rooms hanging off the bottom of the lists of rooms is not much of a real problem.