Yes, that's possible. It could be a cheap Chinese knock-off that is simply not going to work as well as the OEM.
But more likely, you simply blew it badly when you didn't rebuild it properly. Pulling ALL the plugs (coolant AND any oil passage plugs) is simply not optional when rebuilding an engine. That's just asking for the opportunity to pull it out again and do it right the second time.
Not sure what you mean by "cores per inch". A radiator's cores are counted in total, not by the inch. A typical radiator has 2 or 3 cores. Some have 1, some have 4, and I have heard of some having more.
However, contrary to popular myth and radiator company false advertising, more cores does NOT automatically mean more cooling. Radiator design is much more complicated than that. A well designed and well built single core radiator might cool much better than an El Cheapo 4 core radiator.