It is accelerated charge which radiates, and the radiation contribution is proportional to the amount of charge times its acceleration. For a short thin wire or rod antenna, with L much less than a quarter wavelength, I falls away linearly or uniformly to zero at the end of the rod. If the rods have plates at the ends in the form of a capacitor, then the current I may not fall to zero, since it supplies the displacement current drawn from the plates. Even if the rods are capped with plates, this factor cannot be larger than 1. Thus we can make a table for short dipole rod antennas.
L is the total length of the antenna.
Our monopole has radiation resistance of 1 ohm. It also has a large negative reactance, depending on the rod diameter. Also, the higher currents required for a given radiated power dissipate more heat in the resistive loss in the skin-effect of the antenna structure, and so the efficiency drops. Even if the large capacitative reactance is tuned out successfully, the antenna then becomes inefficient, narrow-band, and prone to mistuning and mismatch problems by any alteration of the disposition of scattering objects in the near field.