Also, why is it that the video connection is the only one that is
secured this way? It seems like the power cable would be a better
candidate to be secured with screws. That really could be
A power cable has to carry a significantly higher amount of current than a video connector, so the conductors in your power cable are indeed proportionally thicker. Because of this, and due to the fact that we use metal for conductors, the physical strength of a standard power cable will be significantly higher than that of a video cable connector. Furthermore, it's much easier to damage the tiny pins on a VGA/DVI connector, whereas I'm sure most people would agree it's much harder to bend/twist a power connector (save for stepping on the thing).
Indeed, this is also the reason why many of these connectors still 'screw' into things. Of course it's not a huge deal if the cable falls out of the computer, which is also why you don't have to use the screws if you don't want to. However, it's usually safer to use them to prevent accidental disconnection (saves you the headache of checking behind your computer every time your monitor blanks out), and indeed, a typical VGA/DVI connector lacks the physical holding pressure a standard USB connector does.
TL,DR: This is just an effect of the design, nothing more, nothing less. These cables weren't designed for quick/fast insertion and removal, since it's unlikely to be used quite as much as, for example, a USB port.