OK, this is MY OPINION ONLY; as always, YMMV...
IN MY OPINION, Honda used dual throttle cables mainly to reduce the chances of having the throttle stick open while riding. They also used ridiculously over-sized throttle-return springs, again, mainly to help ensure that the throttle would close properly under any circumstances. IIRC, they installed the SAME (heavy) throttle-return spring on just about every set of carbs they used, regardless of engine size... It's also entirely possible that the Honda corporate attorneys saw ANOTHER benefit to the dual-cable setup; using dual cables probably helped to reduce the possibility of lawsuits resulting from, you guessed it, a stuck throttle...
Back in the day, it was fairly common to see only one throttle cable being used; riders removed the second cable knowing full well what the consequences might be. As long as you know WHY Honda used the dual-cable setup, and accept the risk, however slight it might be, that the throttle could stick open while you're riding, I don't see any reason why you should worry about the presence or absence of one of the throttle cables, which is really only there for a worst-case scenario.
In the final analysis, this is your call; if you're happy with the way things work with only one cable, and you know what to do in case the throttle sticks open, then I for one don't see any reason why you shouldn't run your 350F just the way it is. Over the years, I've bought a few '70's-era Hondas that had both cables installed, and a few that had only one cable, and I never felt the need to install the second cable. I never cared one way or the other if the second cable was there or not; as long as the motorcycle worked as I expected with a single cable, I was happy.
Other might feel differently about this, but if you're not sure what to do about this, just flip a coin, or consult a Magic 8 Ball, and enjoy your ride, whether you continue to use only a single cable, or install a second one. I think that the only REAL benefit to having a second cable installed is that if the pull-cable ever broke, you could probably rig the push-cable to work the throttle, and not be stuck by the side of the road. That second cable would probably get you home without a lot of fuss and bother...
OK, I'm just about finished ranting about the dual-throttle cable setup; whatever you do, don't get me started about the ridiculously strong throttle-return spring... -- kd
