Parallelling existing UF wire to use as feeder
You're rationalizing.  You want to do it, and you are trivializing the many reasons why this is a bad idea, and trying to boil it down to one reason: that it's not allowed for wires smaller than 1/0. And then your logic is "well that's a silly rule, so I can just ignore it". 

One of the wires breaks

The first problem is that if one of your wires (hot or neutral) has a simple wire break, now, ALL the current is flowing on the surviving wire.  That is why you do not just split wires like that.   

"Oh, well, I'll just use two 30A breakers then, so every hot has a 30A breaker".  What about neutral? Neutrals don't have breakers. 

Special equipment

Go read the paralleling rules.  There are a bunch of requirements, but one of them is that paralleling must use custom equipment specifically designed for paralleling.   I have such equipment in my shop.  I have six 1000 kcmil conductors going up to a busbar, 2 wires per bar.  The origin equipment is a disconnect switch with six 400A fuses. ONE PER WIRE.  See how that nicely solves the "broken wire" problem? 

So you too would need "special equipment" at the origin of your paralleling rig, and that equipment would need to give neutral a breaker.  If I were out to violate code and wing-ding that, I'd use a 3-phase service panel, treating neutral as a phase, and fill it with 6 x 30A breakers. But I'd still respect the rest of the paralleling rules. 

You'll be at least $120 into that.  Why did you say you wanted to do this? To save money?