There are several reasons that this topic is so confusing. First, the word "grounding" can mean "earthing" or "bonding" depending on context. By "earthing" I mean connecting some part of the electrical system to the Earth itself. This can be beneficial in the context of lightning or swimming pools or a few other situations.
By "bonding" I mean connecting together normally non-current carrying but conductive parts of the electrical system. For example, the metal frame of your refrigerator is bonded to the metal frame of your stove since both of them are connected to an EGC via their 3 prong plugs. Bonding in this sense is always required. Collectively these bonded metal parts are the "ground" whether or not they are actually connected to Earth.
Second there are three different options with respect to "grounding the system", which means whether one of the circuit conductors is intentionally connected to ground. In an "ungrounded system" there is no such connection; this is also referred to as leaving the ground "floating". In a "resistance grounded system", there is such a connection, via a resistor; this will stabilize voltages between the bonded metal parts and the circuit conductors, but won't allow any significant current to flow. Lastly, there is a "grounded system" in which one circuit conductor is solidly connected to the ground.
Furthermore, there is the question of whether the ground should also be connected to the Earth through a "grounding electrode" such as a ground rod. So we can say that the system is "earthed" or "unearthed".
In the US, residential electrical wiring is a grounded, earthed system. But a floating portable generator without any grounding electrodes would be an ungrounded, unearthed system. Both systems can be safe--for a standalone portable generator (not connected to any house wiring,) it is unclear to me whether there is much safety difference between a grounded and ungrounded system.
With respect to standalone portable generators, I'm not aware of any safety advantage to earthing the system. Maybe there is a scenario with a long extension cord lying on the ground and a lightning strike, but I haven't thought about it.
This thread started because an EVSE that does a "ground check" will not work on an ungrounded system like a floating portable generator. So to get such an EVSE to work you need to switch to a resistance grounded system or to a grounded system. If you believe that for standalone portable generators, an ungrounded system is safer than a grounded system, then switching to a resistance grounded system will let the EVSE work while otherwise retaining most of the features of a ungrounded system. If you don't see any difference in the safety of an ungrounded versus a grounded system on a standalone portable generator, then switching to a grounded system is simpler.