The browser's width is set by scripting codes in the source of the web-page your viewing. If you want to max-out then you have to do it by hand, not many people just wanna display one browser... Normally, if you close a window. Next time you re-open it should open at the same size as you closed.
Personally i like to run iChat, MSN or ICQ while i surf.
I agree with running multiple applications at once, but I am of the same mind that when I maxmize the application, I want it across the entire screen. There are always methods of switching between apps should something pop up that needs my attention.
Yeah, just drag it. It may not stay that big the first time you close it, but eventually it will realize you want it that large and will continue opening it at that width. I like my stuff full screen too.