> Why is Neutral grounded?
See Doug's post about his house hit by lightning. If there is NO ground on the house electric system, even a slight near-miss will induce all the wire to HIGH voltage, sparks jumping out of the walls, transformers break down. Grounding some point on the house wires gives such surges a place to go with less harm. Conversely lightning on the street-poles tends to go to ground rather than through the house. (In Doug's case it was a real HIT and no practical ground would have saved his well-pump or PCs.)
And for assured fuse-blow when a live wire touches ground or groundED cases, sure. (There are systems run UN-grounded when the damage from a blown fuse exceeds the risk of a "live" case: steel-mill motors are the main example. These need Special Supervision.)
NEC requires ALL conductors to return to dirt via approved paths. A strict reading would include aluminum siding (there is a case where siding got electrified by a nail through a wire and nobody knew until someone leaned a ladder against it... if the siding were grounded that nail would have blown a fuse and forced investigation).
You obviously can't ground all 2 (or 3) wires in a power line. Pick one and ground it; the other(s) will be forced to a known reasonable voltage relative to ground. We like to stay within 150V of ground. We also like the copper-savings of 240V power on large loads. 120V-0V-120V grounded in the middle gives us both.
> So what would/could happen, in a (3 wire power cord) Fender BF Bassman for example, if the Neutral was not grounded?
You don't care, but.....
Probably no problem at all, in most cases.
Perhaps a rise of hum, though if all the wall-wires are on the same floating ground, probably not.
Bad shock if _anything_ on the circuit has a ground-leak and you touch the Bassman and a ground (pipe, dirt, concrete). If the house wiring were truly ungrounded, and the pole-transformer had stray leakage to the HV line feeding it, the whole house "could" rise to 13,000 Volts away from dirt. That's enough to pull shocks through wooden floors.
A fair number of US homes are NOT really grounded. Often there is no clue, at least if you are not suspecting a problem.
If you are floating a studio.... it's illegal, it's confusing to everybody else, insulation break-down is a serious worry, you better be SURE there is NO path to external ground.... but yes, you can run a power system totally-floating from the world, just like a flashlight or airplane.