Why are ground wires required to be so large if a short results in an immediate breaker trip?
Total heat notwithstanding, wires also have resistance.  As in "ohm" resistance.  

What you may not be understanding is breaker trip curves.  Breakers have a thermal trip mode from 1.0x up to about 10.0x breaker rating, where the action is delayed as a bimetal strip warms up.  This is to be permissive of motor starts, inrush current, or "toaster and microwave at the same time" short term overloads.  The thermal trip is sized to warm at about the same speed as the wire in the walls, so it trips somewhat before the wire warms enough to be dangerous. That requires matching between breaker and wire size. 

Breakers also have a magnetic trip mode that instantly trips at around 10x breaker rating. 

With too-small a ground wire, the breaker cannot magnetic-trip because it cannot flow enough current to hit 10x, because of the too-high resistance of the wire.  And as you can guess, that's trouble. 

Now we're in thermal trip mode.  We have a 70A breaker's bimetal strip, in a race with a #14 wire to see if the breaker trips before the #14 wire hits Fahrenheit 451.  Obviously, the breaker is going to lose.  



Now as a stupidly practical thing, one way you can solve this is do the big stuff in EMT or other fixed metal conduit.  In those cases, the steel conduit and boxes are the ground path.  And steel conduit has such good conductance (1/resistance) that it can ground pretty much any wire that will fit in it.