Say I'm on Twitter's web site. Most of the time, I just want to browse tweets. So don't pollute the site with a new tweet from that I rarely need. Sometimes I want to send a tweet though. Refresh the whole page (with a trip the server), just to pop up a new tweet form? I want to get back to my Twitter stream after this tweet. Just put some UI front and center so I can focus on that one new tweet.
Modal dialog boxes have plenty of good uses. But most of all, they're an option. Another tool to use.
1. The simplest solution to the problem you described is to have a simple link to the new tweet form, which the user would middle-click to open in a new tab. It requires no fancy coding and allows for remarkably smooth workflow.
2. Does your server demands a human sacrifice for every request it processes or something? And if so, do you not include any images, fonts or script files on your pages and inline everything?
3. Modal popups don't just display new information. They block access to everything else in the window. In the wast majority of cases doing that is pointless and stupid. The evolution of Firefox UI is a great example of how much more usable modal-less interfaces really are.
Modal dialog boxes have plenty of good uses. But most of all, they're an option. Another tool to use.