This was a big thing in Counter Strike 1.6 due to it giving you in-game advantages. For example, all leagues eventually started requiring you to use 32-bit graphics because people were using 16-bit graphics to be able to see through smoke grenades. If you ran the bare minimum settings, you would be able to minimize the distractions and increase the contrast between players and the level, letting you focus on winning.

The main reason pros will use lower settings for CS:S or CS:GO is because it is incredibly important that the game runs perfectly smoothly so that it reacts consistently to their input. Since everyone is on 144hz monitors now, that means they will need to stay above 144fps at all times.

Now, most CS pros who are sponsored will have good hardware and can do this on 1920x1080, but the problem is that at LAN tournaments in foreign countries, it is much less common that hardware which can do this is available. So the pro players will purposely use something like 1024x768 because they know 100% that the computer they will be given at any tournament will handle that, and changing something like resolution would take a few days to get used to and they won't get that chance.