Yes, you can write arbitrarily short blog posts. But you don't, because you feel like you have an obligation to make your official blog be a well written, safe-for-future-eyes snapshot of your personality. Most of us have started a blog with grand intentions and given up after the effort of crafting essays carefully became too much.
Twitter requires no more commitment than a minute of your time. The simplicity of the medium (http://www.flickr.com/photos/jackdorsey/182613360/) is its greatest strength, and it is also why nobody else was able to make it. It takes a special sort of daring to provide a product that does so little. I'm sure users are constantly clamoring for the 140 character limit to be lifted, for new features to be added, and for more in general. But if Twitter had been created with no emphasis on short, simple messages, it would've been just like all the other blog ecosystems.
The impact of the small commitment goes beyond the importance to the average user. I think that one of the huge factors in Twitter's success was all of the hype generated by celebrities. What better way for celebrities to connect with their fans? They can do it in the privacy of their home, it takes nearly zero effort, they get extra points for being tech-savvy, and they cut out the middleman of the media. For the star basketball player who think he's misunderstood (e.g., @TheRealShaq), this is perfect. No more media twisting his words, just one-on-one conversation. Except it's better than one-on-one, because the whole world gets to see how you treat your fans.
In short, I think Twitter took off because even though they didn't know it yet, people yearned for a low effort medium of communication.