I think it would be pretty much impossible to build a practical symmetrical full wavelength dipole. The feedpoint impedance would be very high, my guess is in the >1K ohm range. You'd be thinking 9:1 balun to get anywhere close to 50 ohms and I would still assume you need an antenna coupler. Off center feed would be mandatory!
OTOH, if you make a full length /loop/, that would be a very acceptable antenna. The reasoning behind a full wavelength dipole would be to move the lobes from broadside to the ends, but not much advantage otherwise that I can think.
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