essentialism. Types were
held to be the exemplars of some taxon (for
instance, there was
commonly a "type species" for genera in the early
19thC), but they
did not have to bear all the characters of the
taxon's other members.
Every Linnean genus still requires a type species -
the one which is first described as member of that
genus or in cases like splits a newly designated one*.
Hence "name-bearing type". If you consider a genus a
clade (which it should ideally be), the type species
is the subclade where whe containing clade of which
bears that name if not a junior synonym. Thus, if the
type species gets removed from a genus, it takes the
genus name along with it. At least that's how it works
in zoology, but I think everywhere else too.