@lemelman, you are correct. It should be possible to construct almost all of this assembly with revolute joints. Whether this is the best method to construct it or not doesn't matter to me. It should be possible to use Revolve, and if there is a bug in Joints, it's worth looking into.
I think that there is something wrong with how the joints in the model that you shared were created, and, as I went through the exercise I think I figured out what the problem is. Sometimes, when I open that model, and Compute All, I get lots of failures and the assembly goes all wonky:

So, I deleted all the joints and Capture Position features, and re-assembled it using Revolute joints. First, I positioned the components relatively near where they should be. I do this as a practice, because I've found that it is easier to create the joints this way, and also because I've found that the solver is more tolerant if the components are close to their final positions. I have no idea if this is a real thing or not, but I do it anyway:

Then, I created the Revolve joints, taking great care to pick consistent geometry on the pipes and connectors. I used the inner edge of the connector, and the outer edge of the pipe. Again, I've found that if you are consistent, it helps:

When constructing the base, I found that creating the last Revolute caused an error:

I now understand why this is - all those Revolute joints cannot be free to rotate in a closed loop like this. In fact, now that I think about it, I suspect that is the root of the problem in your original model. Though it seemed (even to me) that it should be possible, once I started thinking about it from the solver point of view, I understand why this is hard. The solver wants all those pipes to be free to rotate, but that last one in the loop will make it so that none of them can really rotate. So, for that joint, I would use an As-Built Rigid joint.
Then, I added the revolve joints for the "curve" components, and now it all functions well. I attached the model, just for your reference.
Hope this helps, and I apologize for the overly-long answer - I kind of wrote it as I was doing the experiment, so I discovered things along the way.
Jeff
Jeff Strater
Engineering Director