Is there a lot of value in learning to write Chinese characters?
You're right that most of the time, you use a computer or cell phone when "writing" Chinese characters. In fact, many Chinese will tell you that - beside their own name (used as a signature) - they almost never write any Chinese characters by hand.

Today, writing Chinese characters is more for memorization than for practical purposes. You might know a few characters and you might know how to type them in your computer, but the only way to really keep them in your mind, and being able to read them fluently, is to write them. It is however rather tedious so it works better if you have some interest in Chinese characters to begin with, otherwise it might get boring.

The best way might be to just try. Write a few characters every day and you might find yourself interested in all the subtleties of Chinese characters.

Edit: There's a related question about the relation between writing and memorizing on the Cognitive Sciences Stack Exchange - https://cogsci.stackexchange.com/q/68/63