Will there be occasions when using 2-pin plugs is safer than 3-pin plugs? Is it accurate to say that 3-pin plugs are always safer given the presence of earth?
That is actually an interesting question.
The truth is... it is complicated.
Consider the following three connection systems.
The first is your typical appliance with a three pin plug and a grounded case. If there is a short from the live line to the case the line is shorted out and hopefully there is a breaker in there somewhere that will trip. This type of connection will prevent you from being electrocuted, but may cause overheating and a fire in the cables if the breaker system is not up to snuff.
Option 2 uses two pins, that is no ground connection. Obviously if the case is metal and there is a short to the case, you will be electrocuted if you touch the case. However, it is usual for such devices to be double-insulated such that two insulation faults must occur. Alternatively, all exterior parts should be non conductive. However, none of the latter is guaranteed, especially with cheap stuff like table lamps and the ilk.
However, the only reason you get a shock from option 2 is because the power system is referenced to ground. The third illustration shows how, in an isolated power system, you will not get a shock from touching the case since ,by doing so, you will not complete a circuit back to the transformer. In order to be shocked in this system you need to touch both lines.
So, that should take care of your electrical question.
As to whether the country is any safer, that is a whole different question.
It is important for all devices having same potential in the environment under consideration so that there would be no voltage and currents between their chassis, and when human touches two unconnected devices, s/he would not get electric shock (I do not consider electrostatic charge here which is another story).
Having everything connected through PE which is provided within 3-wire plug is one method removing the risk. But in such environment is it essential that all devices must be connected to this PE wire properly.
In two-wire power setup potential leveling is performed differently. The chassis potential is generated internally to the power supply. For example, you can find service manual of TV set KV-29FX66, and on page 36 you can see its power supply diagram, where you can see that there's a network of capacitors C6003/C6004 and another network based on C6013/C6013/R6013 form this chassis potential relative to the mains. If all devices are having same circuit inside we can expect that there's ideally no potential difference between two unconnected (to each other) devices' chassis, however most of the times it is not the case, and difference in potential may be up to half of input AC power in case circuits differ or one of the circuits is faulty.
That's why, if you had experience working in 2-wire supply systems, you very often may have even a spark between chassis of devices you connect live. I, personally, always disconnect devices from mains in such setup before interconnecting them.
Answering your question: 3-wire plug is safer, but only in case grounding is performed properly. It is possible to get injury if one device is grounded to PE and another is not.