I agree it is by product but more likely a by product of the twisting and curling of dimensions than just EM
The issue people have is trying to define it all using 'physical' things, physical properties. Many forces have no charge, no mass and are not downstepped into the physical 4D realm. The Higgs field is the field that allows the creation of the 'physical' The EM appears to be a 'physical' field that must have charge.
overlapping fields - I am sorry you can't understand fields with no mass or charge.