This is going to be a really long rambling answer because I won't know what I think until I see what I say. (Edited to add: TL;DR -- I'd like two separate rooms. I originally suggested flipping them, so that the Weekly Topic chat takes place in Roots, with a weekend BS session in a separate Weekend room, but now it seems better to leave Roots as-is and hold the Topic chats in their own room.)
One difficulty with using Roots for me is that I never know who (if anyone) is around to chat. I know that when I log in and check the site for new questions, I forget to swing by Roots and join the room so people can see that I am here, and I don't think to look if anyone is in the chat room. I am still used to forum software where you can set the board to automatically show you are online if you don't want to be invisible. I think for the weekly chat, I have seen notices on the right-hand side of the page where the Related topics and the 'Featured on' box are displayed, but I don't know the system well enough yet to know how all that works. So for me, part of the decision about what to do should be driven by how SE's software works.
The one time I've really used Roots in a big way is when Dave Blackston and I were getting into a tennis match in the comments to his question, and I asked him to meet me in chat. The system was about to send us into a dedicated chat room, which would have been okay if we were only working his problem, but I wanted to talk to him about methodology, so it was really a commentary on all of the questions he had posted so far, and there were (I hope) ideas tossed about that might be useful to someone else coming along later.
The other posts I've made in Roots have been a couple of news items I just tossed in for people to see if they stopped into the room, because no one was around when I made them, or if I wanted to ping a specific person (e.g. telling JustinY about Find-a-Record getting talked about).
The idea of moving the chat with a topic to the main room, and having it all week long, is intriguing. One advantage: we have had a recent visitor whom I suspect has been coming by to chat primarily because he wants to practice his English skills. He has said that he stopped by because he saw people were in the room. PolyGeo and I have been steering the conversation back to G&FH topics as much as we can, but it is a slog, because he seems to be more interested in ancient history.
If the chat-with-topic is held in Roots instead, it might be easier to sustain a conversation about the topic of the week because Roots might be less attractive to random people who just want to chat about anything.
However, the downside might be that if someone had a situation like Dave and I did, there would no longer be a general chat room to go to, and that off-the-cuff talk would collide with the on-topic conversation.
I would not like to see the weekly chat -- that is, the current chat-by-appointment chat setup -- go away entirely. Random visitors aside, it is useful to have a time when you can look in and perhaps have a greater chance of finding someone there. I know it hasn't worked out that way so far, but I was hoping that the monthly workshop chat could be an incubator for Q/As. A weekend free-for-all BS session in a separate room could be a useful compliment to the on-topic-chat.
My other feeling is that it won't help to move the weekly-topic-chat to Roots unless people are willing to say something even when they are the only person in the room. Otherwise, it will be like the Saturday chat is now, where people come in, see that no one else is there, or active, they say nothing, and they leave -- only instead of that happening over 24 hours, it will happen all week long.
So, to sum up: I would still like to see a separate room for chatting about things which are not about the specific weekly topic. I propose that if we move the on-topic chat to Roots and have it last all week, that there be a separate free-for-all room, perhaps all weekend long, that could be used for workshopping and other current events that are outside the Topic of the Week.
Edited to add: As I write this, I see two boxes on the right hand side of the screen underneath the message "125 People Chatting" and two boxes, one for each chat room, displaying the information about the last posts in each chat room. I don't see these boxes or the messages about the chat room on the main site. Might we get more users in both chat rooms if this information was displayed on the main page in addition to on Meta?