I don't think that's the reason collodi went to DMH but I think nexus is the closest thing to a replacement for that play style.
I think you've very much put collodi in a box there. Although collodi was a very good control obey type master like zoraida or lucius, that was by far not his only trick. The summons were quite important imo for instance. I think a testament to their differences is that all of them were neverborn masters and yet they all had their own place.
I do agree that collodi has similarities with them. However, I would argue that nexus has a larger amount of similarities and has a similar feel for the reasons I gave in my last couple of posts.
P.S. I'm not a big fan of collodi in m3e. He just feels a little lack luster. Which is why I'm so excited to see the rest of the cadmus crew.