I doubt "huge" is the proper adjective given that Iberians today in some analyses have only 25% steppe.
Before the BB came in the local population was zero steppe and the BB themselves, even in many parts of Central Europe, had no such high steppe ancestry percentage to begin with. If you check the Southern French BB which were the source, you will see that they are even lower and in later times Iberians got admixture from the North, but also from the South with less steppe. If taking everything in account, you end up with roughly half the population being replaced autosomally and 95 plus percent on the paternal side, I'd say that's huge.
Its not about "steppe ancestry" but Bell Beaker ancestry.