Szczepan Bialek wrote:
Remember: The grounded leg is the radial.

You think that because one end of the coax has its shield grounded,
the other end has its shield at ground potential.
That is not true. At radio frequencies, there can be a potential
at one end of a conductor even when the other end is grounded.

It will result in a radiating outer conductor of the coax, but not
in a grounded leg of the dipole.