The chances of my primary failing are slim but having a pistol allows me me the option to use it if necessary; more likely to pass my pistol to a team mate when their primary fails/out of ammo in order to keep them in the fight longer (instead of an early trip back to the safe zone). I do have a lanyard attached to my pistol in the event of it falling out of its holster.
Depends on the site and the game. I like to carry as little as possible so in a CQB skirmish will often just have either the rifle or the pistol. Playing with pistol only is great fun, does put a smile on the face, as it adds a different dimension to your playstyle and tactics employed.
Are they a necessity? It is all down to personal preference. However, I think that when starting out it is best to buy one better quality gun instead of getting both a rifle and pistol. And then buy yourself a pistol at a later date. As a rough average the pistol only gets used 10% of the time compared to the main gun, so it is more practical to invest (especially with a limited budget) in the main gun first.