Kathy Perkins tried to send the message below to the list, but it didn't
pass through. I'm grateful for this and other answers to my question.
Now I see the situation more clearly.
The difference between the PhET sim and Khan academy is that in the PhET
sim we model the band structure of the electrons. Because the electrons
are filling a band and because the band has a definite range in energy,
whether an electron will escape or not depends on the relationship
between the frequency/energy of the light and the energy of the electron
that actually absorbs the photon within the band. We are only talking
about the top most band, but electrons lower in that band will need more
energy to escape than electrons higher in that energy band.
Electrons will first start escaping when the photon energy equals the
energy it takes for the most energetic electrons in the band to escape
the metal. However, when you shine light of this frequency onto a metal,
some of the photons will be absorbed by electrons lower in the band and
they will then not have enough energy to escape and be kicked out. As
the frequency of light increases and the photon energy increases, it is
more likely that the photon energy will be able to kick out an electron
in the band no matter what the energy of the electron is in the band.
If you simplify the model of the metal and ignore band structure and say
that all photons will be absorbed by the most energetic electrons, you
get the behavior that Khan academy explains ... each photon always
leading to an escaping electron. You also would not get the range in the
electron kick off speeds that we show. All electrons would escape with
the max velocity.