As according to everyone the web shall displace desktop apps in about every area, this means that really complex web application must be able to run.
A slow browser will only lead to the webapps we have today which are not very complex in comparison to full fledged desktop apps (see Google Docs vs. Office, Mailclient vs. gmail, etc.).
If browsers continue to perform that different and also continue to implement different features with different syntax, where will this lead? To web apps that are built for the slowest browser and the most minimal features available. The only way out of this dead end, that i see are web applications that are just browser specific (aka "The website was developed and tested with browser XXX. Please download XXX _here_ or continue on your own risk").
And both ways sound horrible to me. Look at some HTML5 "tech demos" and see what web apps could be capable of and then look at the web. We are still years behind and it will take several more years to have web sites that implement new features.