Some reasons I'm surprised weren't mentioned above:
1) Written stroke order is still the primary system for looking up characters in a dictionary! Yes, you can break them down by radicals & composition, but if you don't know stroke count/order (because you've never written them yourself) you'll likely fail to find what you're looking for.
2) If you live in China/Taiwan, you will fill out paperwork by hand (bank forms, visa applications, rental agreements, post office, hospital forms, school papers). Even if it's just your name & address you need to know how to write it properly. If you live there and have never done this, it's probably because somebody else did it for you.
3) If you always write in pinyin, you probably think in pinyin, which isn't 100% accurate for pronunciation and isn't helpful for differentiating new homophone vocabulary. Using Taiwan's Zhuyin phonetic system (BoPoMoFo), you see that "wen" and "lun" actually use the exact same vowel sound, not different ones as shown in pinyin. Do you think seeing 'e' vs. 'u' might subtly affect your pronunciation?
4) If you always use computers, you'll rely on computers. This is tough to avoid as apps like Pleco make real-time look-ups almost effortless, and phones/laptops show a convenient array of options to jog your memory. Convenient, but this also means you're not really literate - you're just good at looking things up (see #1 above); also you're screwed without your gadgets.
5) Lastly, as has been said, writing by hand has been shown to help with recall. It adds a kinetic component that your brain can hook into for added context. It also forces you to more deeply process the information than you do when merely transcribing. Research has shown recall and conceptual understanding isn't as strong with keyboard typing alone.
All that said, you can always learn to read/write on your own. If you want to focus on speaking & listening, focus on that - those are much harder to do w/o partners & teachers anyway.
...After typing all this, I see the OP was from 2012 :\ Zombie thread necromanc'd to the top of the pile today. Meh, I stand by my opinions - Yes, there's necessity & value learning to write Chinese :)