Indeed, and you can argue to your heart's content over past regimes. The point is that the claims that not buying a striker was our doom turned out to be incorrect, and we didn't lose a title because we couldn't sign the one we wanted. We could also have a long talk about probability and the randomness of events in sport, but that would involve both math and a willingness to get off narrative high horses.
Had we had a decent alternative when Kane was firing blanks at the start of the season who knows what might have happened? No, it wasn't our doom, but it wasn't sensible either. We winged it to a certain extent.