You need to understand that 0V is not special. It is just a defined reference. When we say a plane is flying at 20,000 feet, that number is meaningless unless you also specify the reference; is the plane flying 20,000 feet above the ground? 20,000 feet above mean sea level? Or at a level of atmospheric pressure equivalent to 20,000 feet above mean sea level on a standard day? (Answer, all of the above get used in different contexts.)
It is the same with voltage. You either give the voltage difference between two points, or you give the voltage relative to a defined reference.
The loads connected to a transformer don't care about the 'absolute' voltage of any point. All they care about is the voltage difference between the terminals. The load doesn't care about the connection to the earth, or which conductor is the grounded conductor, or even if there is a grounded conductor (with an important exception that I will get to below). All the load cares about is the voltage difference between the terminals that it is connected to.
The exception is that the insulation system of the load usually does care about voltage to ground. In normal operation, current is flowing through the load terminals, but if the insulation to ground fails then you will have a ground fault with current flowing to ground. That is why limiting voltage to ground is important, but it isn't essential to the normal operation of the load or to normal current flow.
We intentionally create a solid connection between one terminal and soil to force the system-ground voltage to a desired value, and to provide an intentional fault current path. But the loads don't care about the system-ground voltage during normal operation. Sometimes systems are intentionally left ungrounded to create a system that can continue operating even with a single ground fault.
Think about it: transformers work just fine on airplanes. If you had a long enough set of meter probes, you might find that the aircraft is at thousands of volts to ground (probably DC); but internally everything works just fine with the 200V 400Hz 3 phase and 28V DC. The shell of the aircraft is used as the local reference (and usually called 'ground', but clearly it has no connection to earth). There are specific other situations where you will find low voltage transformers 'referenced' to extremely high voltage. An example are the tower lights on AM radio stations. The tower might be at thousands of volts relative to ground, but the lights are supplied with 120 or 240V. They use a special high isolation transformer that derives the 120 or 240V even though the 'local ground' is thousands of volts relative to the nearby soil. ( see
https://www.engineeringradio.us/blog/2011/09/tower-lighting-transformers-isolation-chokes-etc/ )
If you have a typical 480/277V wye system, and disconnect the earthing connection between X0 and ground, you will create an ungrounded system. The system would probably continue to operate normally, and typically the voltage between X0 and ground would be low. But without the intentional ground bonding the voltage between X0 and ground is set by things like leakage current and capacitive parasitic current, and during fault conditions the X0-ground voltage can be just about anything. If you have a solid phase-ground fault, X0-ground will be forced to 277V, and during some intermittent faults the X0-ground voltage could be above 480V. Ungrounded systems have a history of cascading failures where one fault pumps the system to very voltage relative to ground, and the high voltage causes insulation to fail.
-Jonathan