A slow and inadequate standards process led to the browser wars. There were no standards for doing what people wanted to do with the web-- so instead of waiting for the WC3 committee (or whatever it was back then) to come up with a standard way, the two major browser manufacturers decided to do it anyway. And it's no surprise they did it differently. However, if the WC3 had provided robust standards early on for dynamic content, proprietary solutions would have been at a disadvantage.
However, flash fills the missing piece of the picture. In the late 90s, flash was not as robust or ubiquitous as it is now, and website developers had to use proprietary HTML extensions to provide dynamic content to their users. But now, with flash as widespread as it is (adobe claims around 95% of computers have flash10), website developers use it instead of proprietary extensions. Flash has become, in effect, the standard proprietary extension to HTML.
If you want websites to stop using flash, provide a standard that does what the websites need, and sooner is better.