I have used balanced feed line before, although not for a single band. Its strength comes from being able to use it to tune a wire antenna to multiple bands. It does this by having almost no losses, which allows a matching circuit to be on the radio end as opposed to the antenna end.
I have suggested using balanced feed line once for the CB band, but that was for an excessively long run of around 1000 feet (literally up the side of a mountain), where even the much vaulted LMR400 will have near 75% loss, but 450 ohm window line will only have about 30% loss. So there are situations where something like this could potentially be useful.
If you want to use parallel feed line to learn or just play with, I will not tell you not to, however running parallel feed line does have requirements of its own. Its lot like coax where all the energy is kept within the shielding, and this energy in fact exists in the area around the feed line, so you need to do things like keep it away from longer runs of metal, and burying it is a bad thing.
If you want to run 450 ohm window line, you could put a 9:1 balun on both sides. In fact, almost every time a balanced feed line is run a balun exists somewhere in the system, typically there is a 4:1 balun in the antenna tuner. Other "balanced tuners" act like a balun in and of themselves.
I have seen a thread on another forum (not a nice one mind you) where someone talks about using half wavelength multiples of parallel feed line on the CB band to non-balanced vertical antennas, however again, you still need to run something to balance both sides of the feed line as an imbalance in currents on the parallel feed line will treat the feed line as an antenna and radiate (just like common mode currents on coax) which would defeat the purpose.