How does Starving help?

There are 2 things that affect bonus level to a max of 50%-1 lvel AKA perfect tamke. One is making sure the critter does not loose health after taming starts, and second the number of bites taken. For every bite a small portion of effectiveness goes down, which is why kibble gets you better tames - fewer bites till tamed.

Starving without using any drugs is done mainly to be sure nothing attacks the creature AFTER taming starts - which would lower tame effectiveness. Then once starved the critter will eat all the food at once minimizing time it would take to get injured. The time to starve is exactly the same length as the taming time would be without starving, so no time savings.

Using the Hunger elixir, you can dramatically speed up taming time, becasue after the creaure is knocked out, you can give it the elixir and it will get as hungry as it would after waiting for 5min to an hour depending on server settings. Then you can give it food and it will eat all of it at once. Server settings determine if you will need to give it a single serving of starve elixir or if multiple servings are needed to insta tame.