The only purpose in laminating cores is to reduce eddy loss. Ideally it should be done is such a way that it has the smallest effect on the flux path.
If you laminate in the direction of flux you will increase the reluctance drastically and have something that is very much less effective than high permeability iron.
Two methods are common, laminating at right angles to flux flow is always adopted in some form. Normal motor laminations are built as you describe. In transformers and specialised electrical machines you will find magnetic strip wound into toroids and again the flux path is not disturbed but the laminating process is at right angles to that used in normal motors as it is impractical to wind the tape on edge.
Wire was often used in the early days and this is very similar to the tape method but the permeability is not so high as the stacking factor is not so good.
It is probably the introduction of air gaps into the flux path that makes powdered iron cores pretty ineffective, that and the low stacking factor of the iron component make them poor alternatives to the normal laminated low loss core materials.
You will be surprised how little you need to add in the way of resistance path in these laminated cores. manufacturers use special coatings to guarantee the low losses but in reality many small machines work perfectly well with stacked laminations with no coating. The contact resistance between adjacent laminates is only at a few points and this is enough to break the loop.
High tension magneto cores and many universal motors have no specific insulation applied to the laminates. Using thick tape between laminates or strip wound cores wastes valuable stacking space and reduces iron cross section with no gain in the eddy loss.
Flux
