How did we let this happen?

How could we not have done? When electricity was first being proposed of a way of powering homes and industry we couldn't even agree on a standard for distribution (Tesla vs Edison). The world's governments didn't step in because this was a dispute between private companies. Just like governments didn't decide whether we should use VHS vs Betamax, or drink Coke vs Pepsi.

And then once a country decided on a standard distribution method they had to pick a voltage, a frequency, and a plug/socket design. Again, there was no real reason for governments to get heavily involved at this point - after all, nobody knew if this new-fangled electricity thing would ever really catch on.

Can we just start again?

Sure. But it will cost maybe hundreds of billions. Maybe more than that. It doesn't matter which plug/socket design you say is the right one for the whole world, most of the world won't already be using it (just look at the map!). So all those countries are going to have to change not only the plug on every single appliance in existence in their country, but also every single socket on every wall in every building. And what's the benefit to the countries that have spent al those billions doing that? Absolutely nothing - the advantage and profits will be reaped by product manufacturers who don't have to produce a variety of connectors.