How do I make a website look identical in all browsers?
"Page design should never depend on the page displaying the same for all users. Good design is flexible." -- Bertil Wennergren
There's no harm in making a design which looks more or less the way you intended, in the situation for which you intended it. The interesting part of web design is ensuring that it doesn't break so badly as to become unusable when the browsing situation is different from the one that the author had in mind.
Web designers think that they want the kind of rigid, fragile design that will break into a thousand pieces when the browsing situation doesn't suit it exactly. That wouldn't be feasible even if all browsers were free of bugs in their implementation of CSS and HTML: the fact is that bugs are widespread. They need to think more in terms of tailoring a comfortable garment which will adapt itself to different sizes and shapes, and then they'll be making better web pages.
Unfortunately, this pervasive "identical in all browsers" myth is a widespread conceptual problem which authors find great difficulty in shaking off. Partly it's an inheritance from those who learned their design in paper publishing (rather than in textiles?).