I have all sorts of power tools that are 2 wire. That doesn't mean that there is anything wrong with them, or that they are unsafe. It just means that they are double-insulated.
Unless you have a drill from the 1950s with a steel case.
here's some flowers that could be used at the funeral with one of those.
Sometimes there is confusion about possible shock paths...
A GFCI works by comparing the current going OUT to the load on the black "hot" lead, to current returning FROM the load on the white "neutral" lead. IIRC, if the difference in current out versus current return equals or exceeds something like 4 milliamps, the GFCI should interrupt power. This would protect a person from an inadvertent (or advertent, for that matter!) path from hot to ground via said person. It will not protect said person if they complete a hot to neutral path, with little or no leakage to ground.
A double-insulated 2 wire drill, for example, protects the user by... double insulating! Will have an internal layer of isolation. Will have plastic outers in areas where wiring goes through. Or be double-insulated totally inside, with a metal case or partial case, but that is pretty rare. My 2 year old compound-miter saw is 2 wire, it's steel and aluminum are in the support, rods, and bed area. Motor housing and switch area is all plastic. That doesn't mean that there can't be metal inside. If this 2 wire drill was plugged into a GFCI, the GFCI adds a 3rd layer of safety, action as mentioned above.
So what does a 3 wire add? Why, it adds a "ground" (or as the Brits say "Earth it, Jeeves!")
A 3 wire tool adds "safety" if some electrically live internal part touches a metal case. Hopefully tripping a breaker (but maybe not), if no GFCI, or tripping the GFCI if one is in use.
One could argue the situation that a 3 wire tool that has it's bit/blade/auger/whatever grounded (electrically connected to the 3rd wire) may alert said user to the fact that he/she just drilled/sawed/whatever into a live line, via sparks, smoke, or no workee anymore. Doing the same with a 2 wire tool will result in the bit/blade/whatever becoming live with said line for the time it makes contact, but the user is insulated from that part. It is unlikely that one would leave a drill hanging by it's bit in the wall, and touch the bit. At least I wouldn't.