I've read that the magnetic core can be made from resistive (to current) but magnetic materials, and that the iron silicon sheets are laminated to reduce current in one direction. But wouldn't conduction (in the right direction) in the magnetic core increase efficiency because the current induces more flux? Or would the current passing through the secondary coil cause a field some how countering the intended coupling field due from the primary.. hope that makes sense
You are talking about eddy currents. You may recall that eddy currents will always try to counter the induced change in flux, and in that way they "steal" flux that you would like to use to induce current in the secondary turns of the transformer.
It's easy to see this is a bad thing when you realize that the core will get warm when eddy currents flow. That means energy is going from the primary to the core - and not making it to the secondary.