Does adding salt help water boil faster

The primary reason is for accuracy and reliability in cooking times. Boiling water is guaranteed (not accounting for altitude) to be at 212 F (100 C). With a set temperature you can then say things like "boil X for 9 minutes" with a very high measure of confidence.

You certainly can cook things in the water as you go, but it's going to be a lot more hit-and-miss. Pasta, for example, will begin to cook before it reaches the boiling point. You would need to measure the temperature, and check the pasta regularly to determine when it was done. You can't give someone an accurate cooking time with this method either. The time it takes for water to boil will vary greatly with stove heat output, pot size & shape, and the amount of water.

Adding a starchy substance such as rice or noodles to boiling water increases the surface tension of the water. When it's just plain water boiling the surface tension of the water can't hold back the force of the steam rising and the bubbles burst. Starches increase this surface tension making the bubbles more elastic/pliable (essentially creating a foam), thus requiring more force for them to burst. This makes the bubbles last longer which allows them to build up and eventually boil over.

It's more likely to occur with anything starchy like rice and pasta.

A lower temperature should help to control a boil over as it will allow the water to cool somewhat and slow the boil.

I'd assume that, from your quoted text, that if you use less water you're still imparting the same amount of starch making a thicker solution. More water would dilute this and bring it closer to normal water. In my own experience, small amounts of water allow lots of bubbles to form but nothing really boils over, it just splatters a bit. But reducing temperature and tilting the lid to let some air in has helped me in the past.