Why don't people just go to https://twitter.com in their web browser instead?
The browser window doesn't easily resize to a natural size for Twitter use. The browser either won't remember the size, or it will remember too well and start trying to apply that size to new windows that aren't meant for Twitter.
The browser won't put an icon in my menu bar to show when new stuff has arrived.
The twitter.com window will be mixed in with the others, so cycling through them with cmd-` will be annoying. Conversely, getting to that window specifically will require more work to find it among the others.
Basically, this is a microcosm of why people use native apps at all. The answer is pretty much always "they work a lot better."
Personally, I'd prefer browsers concentrate on being better browsers, not being better at pretending to be real apps. Experience suggests that they'll never be very good at the latter no matter how hard they try, and we already have a perfectly good solution for building something that looks and acts like a native app: an actual native app.
edit: tweetBOT, not DECK, and we regret the error!
*tho it has which has its own frustrations, and totally apathetic devs :'(