I'm not so sceptical about this idea as previous respondents, though I must admit, I don't understand some of the responses.
As far as I can see all antennae have both inductive and capacitative elements and produce or respond to both electric and magnetic components of em fields.
Presumably most are designed on the basis of producing magnetic fields, because all the analysis software seems to work on summing the effects of current elements.
There are people who claim to design capacitative antennae and something called a cross field antenna (described as, " to synthesise directly radiated Poynting vectors from separate
E and
H field sources." ), but these are not widely accepted (to put it mildly!), though G(M)3HAT did get a CFA design published in Wireless World about 27 years ago.
What strikes me as nearer to the OP concept, are the slot and patch antennas. Just as with the above types I can't claim any real understanding of these, but some explanations make them sound like E-field radiators.
(In this link
Slot Antennas the
video (a very informal description) shows the slot having a large E-field and any current effects more or less cancelling.
Microstrip (patch) antennas seems to concentrate solely on the E-field, as does their
video.)
If indeed the basic concept of E-field radiation is ok, then I wonder if it's a matter of practicality that we use current mode antennae?
When λ was 10m - 1000m+ , wires would be much more convenient than sheets (or even grids) of conductor, especially when it needed to be elevated.
And there is the same factor that affects component values in tuned circuits. For efficiency and Q the inductive impedance needs to be high compared with the Ohmic resistance. Which means capacitance values need to be kept small. If you built an antenna with a large capacitative element and commensurately low inductance, then impedances are low and currents and Ohmic losses high.
When I look at making a capacitor to use as an antenna, I keep coming up against the problem of currents. To charge a capacitor requires current and currents cause magnetic fields. However I try to balance these to cancel the net field, the current must go in opposite sense to the two plates. So it could always be argued that the radiation comes from this. (Capacitative radiators are likely to be less efficient due to the effect I mentioned above, so radiation could be attributed to even a small inductive path.) Perhaps accurate measurement of the radiation pattern (and maybe polarisation) could discriminate between the sources of radiation.
It is certainly an intriguing question, but whether it is interesting may depend on finding some practical advantage of this approach. For G3HAT's CFA and DL7JV's capacitive antennas I think the intent was a much reduced size. But I think with so much focus now on UHF and SHF, interest is more in gain, directivity and efficiency.