There's "gotchas" with every encryption scheme - in fact whenever TLS uses any Public Key encryption scheme it'll pair it with a Symmetric Key encryption scheme. So you could say that by your definition no Public Key encryption scheme has "held up" and they've all had to be worked round :)
There are benefits to pairing the slower Public Key schemes with a Symmetric Key encryption scheme using a session key, as you get the benefits of an Public Key encryption scheme with the performance of a Symmetric Key encryption scheme.
There are benefits to pairing the slower Public Key schemes with a Symmetric Key encryption scheme using a session key, as you get the benefits of an Public Key encryption scheme with the performance of a Symmetric Key encryption scheme.