Brilliant! Where can I get one?

The point of not using an electric is so you don't get distracted by playing with a high gain sound. Just a little noodling and pick scrapes before writing, we've all been there.

So your writing on an unplugged electric is the same idea.

I find it easier to work with an acoustic because it's easier to match the volume of my voice and the guitar.

Most of Nirvana's post-Bleach work sounds fine on acoustic anyway, teen spirit included.

I'd probably say it's best to write on whatever you are comfortable in using. An accoustic for writing is great but it all depends on
what you are writing. These days it's all been done so the trick is to present your song in a different way. So now it's all about syncopation and harmony.
It's much better to work high up on the fretboard, finding your triads and working from there, rather than at the top of the neck playing the tired
and worn out C G Am F chords in the normal manner. Unless you are writing "another" accoustic only song.
Different instruments take up different layers. If you wrote a piece on a piano you could easily work out the Viola, chello, violin, brass parts because they all take up
a different space. The viola's would be pretty high up the scale whilst other instruments take up lower parts. Stick those bog standard shapes in on the guitar and often they won't work.
I guess it also depends on what type of music you write too. I would think if you are intending to write a thrash metal song then you will want to hear all that reverb and
distortion and so on to better help you feel in the right mood for writing that kind of song.
Personally I choose whichever instrument I think will better help me write the kind of song I intend to write. If I don't know what I intend to write then I usually play on all of them
until I find somthing I like

Nope... you don't need to play it on anything at all.  At the risk of a huge simplification, we could say we are looking at two apsects of writing: "stumbling upon" and "imagining".  (The reality is generally a mixture of the two... stumbling towards the realisation of something imagined, and/or imagining the development of something stumbled upon.)

We can all picture things in our head that we can't play... for instance, Kurt Cobain surely didn't simultaneously sing, play guitar, drums and bass, while picturing the final outcome of Smells Like Teen Spirit!  (Perhaps he died trying    !)

So my advice would be to practice writing away from an instrument (always go hands-free if you're using one of those acoustic phones in the car!).  If an instrument is just being used as a reference point, e.g. to check that you're really writing down the harmony you think you are, then the sound (tone) of the instrument isn't so important.  For stumbling, use an instrument with a sound that inspires you.

I agree with people that doing what's comfortable. But get notation software! It helps to hear all the elements together at the same.
My personal favorite is Guitar Pro; there's also Tux Guitar and TabIT or Band-in-a-box.

The free trials will help you decide which is best, should you choose one

you gotta go with the flow bro. whatever works for you.

Keith Richards said all the Stones numbers start out as acoustic guitar workouts - take a listen to Brown Sugar for example, you can hear the acoustic thrashing its stuff in the background, probably the guide track? So there you have it, one of the biggest electric rock bands in history are acoustic based!

On a more philosophical note: the electric guitar is a product of the 20th century, it is a separate instrument in its own right; probably the most flexible instrument for the budding songwriter is the piano though, that is a marvellous musical instrument to compose on

also, I find that if you write something on one instrument eg the acoustic and then switch to play it on the piano or something else then you often get something new out of it. I also like writing a melody to some chords and then changing the chords and keeping the same melody and seeing what comes of it. I find it helps me avoid doing the obvious too often.