I can already see that "can-o-worms" beginning to open but whatever... Sometimes there just has to be an end to the suffering...
Odd multiples of 1/2λ will help make the coax "invisible" to the antenna system and when this happens there is a better transfer of power which amounts to less loss and therefore, coiling the coax should make no difference, otherwise if it is cut to something other than odd multiples, the coax tends to become part of the antenna (as in the coax becoming a radiator), which is why the antenna may become difficult to tune and the reason why coiling of the coax has the effect it has... and it just so happens that the higher the frequency you go the more noticeable this becomes (think shorter wavelengths).. Oh and you can forget what I just wrote if cheap coax is used, the skill at attaching your connectors and how "technical" you really want to get about your antenna system...
And if somehow you still disagree, then why is coax used as tuning stubs and how do stubs work? And then you might also want to read up on phasing multiple antennas (think large array multiple beam EME stations) and why coax lengths, velocity factor, type of center dielectric and impedance are important factors to those systems... So with that said, if you choose to use this information you may just find out for yourself that you could have just had a V8!
Oh and it won't matter what type of "tuned" antenna you choose to use, either 1/4λ, 1/2λ, 5/8λ or some type of collinear makes not one iota of difference...
(λ means wavelength and "EME" is Earth-Moon-Earth for those who aren't in the know)