Power Panel Grounding and Neutral Bonding / Dryer hookup in an older home [1975]
Neutral does and should carry normal currents

This may be the crux of your misunderstanding.  

240V loads are carried on the two hots.  120V loads are carried on one hot and neutral.   So a typical dryer might draw 20A of 240V and 3A of 120V.  In that case the amperages of L1, N and L2 will be 23, 3 and 20.  This is normal. 

Ground is a safety shield only

The design philosophy of grounding is that grounds should never be used to handle current.  

The circuit's overcurrent protection already protect from a fault between conductors.  But what about faults between a conductor and anything else? That could cause a lot of mischief.  Ground's job is to be the path of first resort for any wayward fault current. That works really well in metal-chassis machines. 

"Wait. Won't GFCI do that same thing?" Kinda. Yeah. 30A 2-pole GFCI breakers can be had. 

Neutral and ground should be separated everywhere except the designated Neutral-Ground Bond.

In an ideally wired panel, all neutrals land on the neutral bar, and all grounds land on the ground bar.  There is a neutral-ground bond that can be removed.  

This panel can be effortlessly converted to a subpanel by feeding it from another main and removing the neutral-ground bond.  

It is also easy to measure ground fault current, by clamping a meter around the N-G bond. 

However builders also have a lobby with the NFPA, and they lobbied for rules that let them spam it all onto one bar.  It does no real harm, since they're connected anyway by the neutral-ground bond.  It is leeeegal, just is a builder grade shortcut, and obviously prevents any of the things I mention above.

Why not bootleg ground on NEMA 14?

Well, that is what the NEMA 10 type hookup already does, so if that is your intent, there is no need to bootleg NEMA 14... you are already there. 

It's back to the same problem as NEMA 10 and any other bootleg ground - any trouble with the neutral wire will result in the neutral being pulled up to 120V by loads, and with it the dryer chassis. 

Whereas that does not happen if the neutral and ground are separated. In that case the machine just doesn't work and the ground continues to protect against hot-ground faults.   Since there should be no neutral-ground faults, this becomes a non-event except the machine doesn't work obviously.  The broken machine motivates the person to seek a proper repair.  

If there was a neutral-ground fault, the machine may work normally misusing ground as current return.  That is why bad repairmen create neutral-ground faults, to git-r-dun and onto the next job, safety be damned. 

You can  retrofit ground

Under NEC 2014 (and earlier for dryers) it is legal to retrofit grounds.  You can run just a ground wire (#10) and retain use of the existing wires. It can go back to that service panel, or to any other ground also served out of that panel, as long it is of sufficient size (#10). 

This same rule also makes a dryer ground retrofit useful for retrofitting grounds almost everywhere else, so it can be wise to plan it as a "backbone" for other ground retrofits.