Signal integrity analysis is about understanding the analog behaviour of digital signals, such as non zero rise times. multiple voltage instances between 0 and 1, parasitic elements in a piece of copper, or dielectric etc., Understanding of these parameters is very essential because when the signal flows faster in the system more are these issues. Hence the proper reproduction of these signals by the receiver will be a difficult thing.
Secondly, your statement of Signal integrity being model dependent is not fully correct. You can still use mathematical calculations to prediuct the signal behaviour fairly accurate even without having the models. And finally, IBIS is not the only way of SI simulation, there are Spice models, which are much more accurate than IBIS.