It seems I remember that laminated core transformers have better thermal stability than solid core because lamination reduces the eddy effect. I could be wrong though.
pretty much. you don't really want eddy currents, so laminated steel is used.
too many eddy currents will cause the steel to try to turn into a magnet (strongly opposing the change of field direction, and generating considerable amounts of waste heat as the field flips back and forth).
the way the layers are cut, how thick they are, ... effect how the magnetic fields interact with the metal (influencing where they go, and how strong the eddy effects are and in which direction). so, they can help direct the field to where it is useful in the transformer, and eliminate currents in directions which are detrimental to performance.
it is also possible to use ferrite instead of steel or iron, which basically entirely eliminates the eddy effect (and alters its magnetic properties).
the use of ferrite results in relatively little inductance, allowing the direction of a field to reverse rapidly (such as for a high-speed transformer or electromagnet), though results in worse performance at lower frequencies (so, laminated cores remain preferable for things like power transformers).
I am not as sure about motors. apparently ferrite is used in some small high-speed motors. looking into it, apparently it is not as powerful or efficient as laminated steel when used for larger motors.
I am left wondering about the prospects of a motor made with iron-containing 3D printing filament (they basically mix powdered iron in with PLA or ABS plastic for the printer filament), or how this would compare with a person making their own by ordering a large jar or iron oxide dust (to mix in with the PLA or ABS). (the iron-containing filament is pretty expensive at around $15/lb).