Before getting to the meat of the question, I think it will be instructive to clarify on what exactly a voltage is. Voltage is the difference in electrical potential. That is, it is always a relative measurement, taken between two points. Colloquially, you’ll hear engineers and electricians say things like “this wire is at 12v”, but they’re implying a specific reference point. There must always be two points to take a measurement; a multimeter must always have two leads.

Often, that reference point is “ground” (aka GND, aka protective earth, aka COM) but the choice of designating a particular point as ground is always arbitrary. Even the physical soil of the earth is not at the same voltage level all over, which means a ground rod is only a valid reference within a certain proximate area. Instead, ground is often chosen by whatever is most convenient and reaches everything that needs it.

But as you’ve found, having a ground reference is not mandatory for electricity to flow in a circuit. Instead, a ground connection serves ancillary goals, like personnel or equipment safety, or avoidance of objectionable currents.

Comparing floating and grounded circuits, a single loose wire in a floating circuit will not cause a diversion of current to somewhere, because a second wire would need to be the return path. With two loose wires, there can be a second loop for current to flow. A grounded circuit intentionally ties some part of the existing circuit to ground, meaning you are now just one loose wire away from a possible diversion of energy, which could be fatal.

This sounds like grounded circuits would be bad, and would imply that grounding the aluminum conveyor belts in your example would be insane. But this is actually the personnel safety from earlier, if we add the right protective devices to the circuit: a circuit breaker, fuse, a GFCI, or some combination. Those devices will cut out the power source upon a fault condition, and they require a sturdy ground connection to operate effectively. We improve overall safety by having protective devices, and having a robust ground connection.

Finally, I want to offer a piece of advice as you proceed in your studies. The rule that “electricity wants to return to ground” is hogwash. It’s so hideously flawed compared to the true rule, which is universally valid: electricity returns to its source, in inverse proportion to resistance

DISCLAIMER: Not an electrician or other sparky, I just like to have fun with electronics.

“Ground” is only 0v by convention. What it literally is, is, “What ever general voltage potential everything around the circuit has that the circuit could short to.” Most circuits aren’t going to short over air, and any separate circuit can drift in its relative voltage levels to other circuits, so it’s a problem that is dealt with via extra circuitry like a physical ground connection 99.9% of the time.

The entire point of grounding is to both make sure the circuit doesn’t float off to some crazy voltage level that could end up literally sparking to other things, and also to provide an alternate path for electricity if something is wrong with the circuit (like an electrician just introduced their hand to the circuit). To provide that alternate path, ground MUST be at a lower potential than the power source (by convention, since we could have made +v = 0 and shift the whole values appropriately). Relativity is the name of the game.

The aluminum machinery could simply be an older design where both sides of the AC get used as-is, or grounded straight to chassis, or any other number of poor practices which would then require an operator to have their own ground connection to not get the everloving shit shocked out of them for simply touching the controls.

If a metal chassis or metal controls are any part of the circuit, you will have to do something to factor in people touching stuff. Ungrounded or un-looped (not completing the circuit across themselves but simply touching a live circuit) people can still be shocked even on DC circuits because an ungrounded person still acts like a capacitor. A grounded person is simply a resistor instead, but that can easily be the difference between life and death.

And a quick followup:

If the ground was moved to the T3 junction than the battery’s negative terminal would be common to ground and the voltages values across all loads would go back to being positive in regards to the battery’s negative terminal (T1 = 1000V, T2 = 333V, T3 = 0V) ?

I’m not sure if the problem is your post or my client, but I’m not seeing any drawing here.