Wouldn't it be easy enough to let the gates know which train has come
in and then check the validity? i.e. if it's a fast from Surbiton, no
way could a Vauxhall be valid.

That wouldn't work due to the high number of trains coming in and the
fact that people are legally allowed to us any of the gates they can
reach, also those nearer to other platforms. It would be pretty much
impossible to program the system in this way.