Nothing of what you said precludes the ability to have a Brand support. Functionally brands are just like a totem that attaches to the monster that they cast at. So... it's not far fetched to have a brand support.
Just think about the synergy. It oozes with ways to creatively combine spells and brands. Imagine a curse brand. Imagine an scorching ray brand. Imagine volatile dead brand! It'd create a wave of VD across a screen as it kills and jumps to the next monster just in time for the VD to hit them!
Nothing of what you said precludes the ability to have a Brand support.
It does prevent having a support that works the same way as the totem/trap/mine ones, which is what I specified. Those work by casting spells. That means they're separate entities which are actors (able to take actions), with all the knock-on effects that entails (having life, having AI, being able to die, etc).
Functionally brands are just like a totem that attaches to the monster that they cast at.
No, they very much are not. Totems are an entity which casts spells. Brands are a spell - to the extent they exist in the game world, it's only as a visual effect. They're fundamentally something your character is doing. They're like a fireball, not a totem - a spell in progress, as cast by your character.