Its a matter of convenience. A prepackaged software suite will have lots of bells and whistles that you would otherwise have to use several solutions for.
How do you know that the recipe is any good?
The software lets you verify that the recipe meets the style guide lines.
What if there is no recipe?
The software lets you design one from scratch.
Brewing softwware is much cheaper than a calculator that can calculate IBU's according to Tinseth (unless you use online calculators).
Download the Promash trial. It limits the number of recipes you can save without paying, but doesn't expire. This should give you a good idea about what brewing software can do for you. Then you can try the trial versions of Beersmith and Beer Tools. This should let you make a good decision about which (if any) you should buy before you spend any money.
I used to do the math on paper when I first started, and it's good to learn how it all works, but using something like Beersmith makes your life a lot easier.
Do you need brewing software?
No. They don't provide anything that isn't available as information from various sources.
However they combine that information into a nice easy to use package. Provide routines to automatically calculate the results. And provide a nice way to document your efforts.
If you stick to kits, or tried and true recipes then the software is not really that useful. However if you like tweaking recipes or making your own, they are really helpful to provide feed back about what you are doing and give you information about how to achieve mash temps and volumes and boil volumes.
I've learned alot just by playing "what if" scenarios on a particular recipe or style. It really allows you to learn alot about brew styles, hop additions, boil time, etc. without spending weeks or months to actually brew with each different change.
It's hard these days to find the exact hops you need, and even in good times, the alpha acids vary quite a bit. So it's nice even with tried and true recipes to be able to play around with the hop additions to get the IBU's just right given the hops you have to work with.