You're right, you can feed a 1/2 wave length antenna anywhere along it's length and the only thing that changes is the input impedance. But, there has to be two 'terminals', a (+) and (-) for current to flow. If the end of that 1/2 wave length radiator is the (+), then where's the (-) terminal? If there's an impedance transformation circuit used then the output of that circuit has to hav both of those terminals to, so where's the (-) terminal? In either case, that (-) terminal is the feed line (in the case of coax being used, it's the -outer- part of the shielding (at a minimum, at least a 1/4 wave length of it). If a choke is placed in side that first 1/4 wave length, then you've effectively "cut off" that part of the 'other half' of that antenna. Not so good, huh? At least that first 1/4 wave length of feed line does radiate, because both 'halves' of all antennas radiate, even those radials making up a 'groundplane'. Since RF is an alternating current, those two terminals swap polarity each 'half' cycle. The (+) then becomes the (-) and the (-) becomes the (+). Exactly the same for that 1/4 wave length of coax 'stub' on the bottom of a 'Ringo-Ranger', below that impedance matching device (the 'circle' thingy).
The radiated RF field of any antenna is very concentrated at the antenna, there are no 'holes' where there's no radiation. Those 'holes' or lesser radiation areas only develop at quite a distance from the antenna. Doesn't make any difference what kind of antenna you're talking about, all of them have that characteristic. That "quite a distance" thingy is frequency related, as in more than just a wave length or two.
- 'Doc