You cannot choose a group, ok let's be Sumerians, and say we built the oldest civilisation, that is I beg your pardon Dalibor, bullcrap (yes there are close nations that build their identity upon such a method, nonetheless wouldn't got further into the discussion). The tradition, culture, and heritage you inherit, you do not choose, no continuity BEEP you lose, should have fought preserving it. Why the Illyrian group should be the most important, not because it is, hell that group got extinguished 800 years before the arrival of the Slavs, you had Romans, you had Celts, you had Goths, Langobards, Gepids etc. after that, but because of the Illyrian Revival, that needed an umbrella term encompassing all South-Slavs that isn't bearing any connotation like Roman, Goth etc. did bear.
In other words Illyrian is not second most important, Illyrian was chosen because it carried no connotation, in other words nobody knew who the heck they actually were, so they were found suited for a necessary umbrella term, as well as the Roman region was called Illyricum in relation to them. All the crap afterwards with Illyrians, is mythomania, yes of course Illyrians, Gepids, Langobards, Romans, Goths, Celts, Gauls, Thracians, Dacians all inhabited the parts of our current region and were surely assimilated in some moment, but calling it most important is a fabrication. By this argument, the second most important group of the Czechs are the Boii, since they were the Celtic group that gave Bohemia their name.