Smaller tomatoes -- cherry tomatoes, tomatillos etc. -- are fine with the core attached.
If you were cooking a "rough" sauce (seeds, skins, etc), you'd just cook the tomatoes with the cores attached, and then throw it in the blender. Nobody's the wiser. But if you're slicing raw tomatoes for burger and sandwiches, you end up with a fibrous chunky nub on one or two slices.
But during the winter months around here, the tomatoes could all be described as fibrous chunky nubs.