I've checked the Eleutherornis paper recently and I've noticed the only other Cariamiformes they've mentioned was Strygops. I think people pushing for Lavocatavis and Eleutherornis as phorusrhacids seem to ignore other groups of giant flightless carno-seriemas like bathornithids :/
(Commentary for this, I’m guessing?)
I think calling it “pushing” is a bit unfair. It’s just that the current evidence seems to point to the African and European forms being phorusrhacids – the few bones we have show diagnostic features of that group, so the most likely explanation is that that’s what they are.
That said, nothing is ever absolute in science, and taxonomy is constantly being reinterpreted and updated. So of course these birds could still turn out to be something else, such as bathornithids or an entirely new clade of large flightless Cariamiforme which were convergently similar to phorusrhacids. If more fossil material is found, or if somebody does further analysis and comparison of the existing specimens and comes to that sort of conclusion, then we’ll just have to revise their classification accordingly.