Why don't single row circuits work on a breadboard?
Can someone please explain to me why the LED doesn't light up when I try to connect everything up on the same row?


Because you have shorted out the pins by connecting them to each other via the one socket strip line in the breadboard.



Figure 1. The faint red lines indicate the connected breadboard sockets. Note that each row has five connected sockets. Source: Technology Student.

To power any electrical circuit you need a potential difference across its terminals so that current will flow. Connecting them together prevents this and so your LED won't light.

I think that if you think through your thought process you will find that you expected the breadboard row to connect the resistor to the LED but, somehow, not connect one leg of the LED to the other. Would that be right?