The purpose of ground wire is just to carry current in milliseconds enough to trip the circuit breaker, it won't even get hot. So what is wrong with using very small ground wire? For example. You are using #4 AWG in the Hot and Neutral wires (70 ampere capacity) and you use #14 AWG as ground (15 ampere capacity). If the ground is connected to an enclosure and the Hot wire touches it. It would take very fast for the breaker to trip, not enough to heat the #14 AWG. What is the reasons this is not allowed?
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.
In some cases the NEC in the US does allow a reduced size for the EGC. Old Romex cable had a smaller EGC, I think it was 16 AWG on 12 AWG Romex. Since the ampacity charts are conservative for current carrying conductors, I don't think it was ever a problem.
However the NEC only allow limited reduction in size for good reasons. NEC table 250.122 spells out the minimum EGC sizes by breaker size. I would not go lower than these values.
Number one, even in the milliseconds it takes for a breaker to trip, in the event of a very high current fault, the wire can melt or even explode. This is more likely with a smaller wire. If the wire melts before the fault is cleared, you have a very bad situation.
Often breakers don't function as well as they should - I've been very surprised how long some breakers take to trip when deliberately shorted. (This isn't something I would recommend or condone, but someone I worked with thought shorting it was an acceptable way to trace a circuit.) Again, in this situation, the smaller wire is more dangerous.
The other possibility is a ground fault that does not clear the breaker, this could conduct at near or slightly over the full capacity of the breaker for a while - long enough for a very undersized wire to overheat and cause a fire. This should never occur with a GFCI, but like breakers, GFCI's are not perfect.
Under CEI rules your PE, on residential installation, should be at leas as thick as phase conductor. That's because it has to discharge all the current potentially carried by the phase(s). RCD are there to increase the protection, not to replace PE. So it's true that an RCD trips with 30mA current, but it's also true that you don't have to risk a fire if RCD is gone bad and you have a big phase-to-groung failure. Anyway in some older homes you still find 1,5mm^2 PE for 16A circuits (so with 2,5mm^2 phase and neutral).
A fuse, especially a slow-blow could allow enough current to pass for enough time to completely blow off a small ground wire, leaving the device connected to the mains through a nice fat wire, ready to cause death and mayhem.
The fuse should be specified to protect the mains wiring (AWG4 in your case) so it will also protect an AWG4 ground wire, should a ground fault occur.
My answer is a little different than most of the comments.
NEC Table 250.122 and if a service grounding conductor 220.66 gives us the correct ground wire sizes for the corresponding over-current protection and conductor size. In my state we use those sizes because if we don't we are breaking the law. This precludes any other discussion we have on selecting a smaller conductors size, because many people smarter than us have decided what we are allowed to use.
The final comment I would have on the subject would be, if you did not follow the NEC. and someone was subject to a burn or shack hazard that caused damage or loss of life. Then it was determined that an undersized ground caused the accident. Would you be willing to absorb the liability? That's why when there is already a rule we follow it, end of discussion.