Arcane users tap from the 3 realms at once (that is arcane magic). If channeling's power comes from the gods...Archmages are "priest-mages?". Makes no sense.
That has been one of my complaints about the description of Arcane magic n RM.
For me, it is like this (and I tend to use Shadow World as my basis):
Arcane is Essaence and it is the major flows and nodes of the world. (Also called Pure Essence.) Though like Marc R just wrote, it can be tapping the energy directly from its source dimension, that works fine too.)
Essence is the little bit of Essaence that bleeds off the flows, and nodes is present in all things - both lving and non-living - and is more easily used/tapped. (Also called Ambient essence.)
Mentalism, is using the inherent essence that resides within oneself. (Everything that lives in a world bathed in Essaence/Essence is so saturated, and is also called Inherent Essence.)
Channeling is a very contolled/restricted form of essence use granted by a diety in return for worship and service to their cause, but the gods tap the Essaence (Arcane). (This can be known by as many, or more names as their are gods, but universally called (Un)Holy Essence.)
So, Arcane magic is not "all three", but it is the original, much more powerful source of all three. That is why I go with it being stronger and harder to cancel than either of the other three. (Not the "tripod" metaphor, but more of a tree, with the three "realms" being branches and Arcane being the trunk and, even more aptly, roots; it is usually easier to lop of a tree branch, than to cut the whole tree down, certainly than digging the tree up out of the ground.)
I like to think that why essence users and mentalism users have such different abilities has more to do with their training and preconceived notions on how it is
supposed to work, than on the nature of the magic itself. In other words, a mentalist is limited in how many people they can affect and in what way has more to do with what they believe, and not because of the way (method) they tap their personal essence instead of using the ambient essence in their environment. Understanding this, is the first step on the road to becoming an Arcane magic user. Channelers are different because pretty-much everything they can do "magically" is dictated by their god, so they don't tend to every worry about the what's & hows of spell casting, ony the why (for their god, of course, I didn't say it was a difficult question
). (In game terms: 1 PP = 1 PP, 10 PP = 10 PP, etc... so the varying effects are not power related, but mind/belief related. If you believe that a spell will do X, then when you cast it, it will (and hopefully not blow up in your face), and if you don't believe...)