That is the correct definition of antipodal.
Yes, there are lots of broadband antennas, but for the example I cited, you really need a frequency independent antenna. They exist. But I'm not aware of any that range from DC to daylight.
It's not too hard at VHF and above. It's the LF to HF range that gets challenging. There are 6 octaves from 1 MHz to 32 MHz and 11 octaves from 1 MHz to 1 GHz. Or to put it another way, it's 6 octaves from 1-32 MHz, but one octave from 32-64 MHz. You can always achieve a match at the price of low radiation efficiency.
And, yes, I am probably crazy. I just spent $800 on antenna theory books because I did not like any of the broadband HF antenna designs I saw for sale.
I have no idea if what I outlined would work. I also know that neither does anyone else, though I'm certain there is no shortage of opinions. So it seems like an interesting project. It *will* work at some power level. The question is how low a power level will still work.