Combined answer...
As "Avialae" was originally defined on the basis of apomorphies
Oh no, it wasn't. It was defined in some branch-based way that I have forgotten, maybe as everything closer to modern birds than (to) *Deinonychus*. Shortly thereafter, the original author (Jacques Gauthier) changed the definition to a node-based one, the MRCA of *Archaeopteryx* and modern birds plus all its descendants. It was only in 2001 that Gauthier (with Julia Clarke) changed the definition to an apomorphy-based one: the first organism which had wings (with wing feathers) homologous to those of *Vultur gryphus* and some tinamou species, plus all its descendants.
Note that this apomorphy-based definition has no more problems with convergence than any other phylogenetic definition has.
Funnily, the authors of *Xiaotingia* have returned to the original definition, and have equated Avialae, not its crown-group, with "birds".
Look, there's already a good, well-thought-out solution. Use neontological names for crown groups. Do it everywhere in biology. Maximize cross-disciplinary understand. Limit unjustified inferences.
...and open the way for unjustified inferences in the other direction, where plesiomorphies are extrapolated too close to the crown.
Is it really a good idea to maximize cross-disciplinary understanding at the expense of intradisciplinary understanding by making unneeded breaks with history? I'm all for bloody revolutions, but I don't like it when they're bloodier than necessary.