Until you look into the physics and educate yourself on this, discussion is pointless...
Granted, as you say, "it's more complicated than that," and I understand that. However, complication isn't an excuse for out-of-hand dismissal. IE, it can be that there are a hundred currents all interacting, producing magnetic fields (a force between the currents) and feeding back on themselves, but that doesn't negate the existence of the currents, just means that their interaction is complicated.
NO ONE other than you is claiming that the current is being ignored! The current density, J, is included explicitly in the magnetohydrodynamic (MHD) equations...
You keep claiming that the current is neglected, this is a false claim that demonstrates complete ignorance of the physics... It is extremely difficult to have a discussion when you are basing your comments on assumptions that are absolutely false.
You need to educate yourself about MHD if you want to talk about this topic- your assumptions are false and that makes your comments gibberish. This has been pointed out to you before, but you seem unwilling to educate yourself on this topic.