It doesn't feel native to the browser
Most advanced javascript apps don't feel particular native to the browser either because HTML still lacks basic widgets like a combobox or -button. How many native browser buttons do you see in your Gmail or Google reader interface?
It's not aware of browser resizing - you're locked into a fixed width layout
Wrong. Flex handles browser resizing out of the box, see for example http://www.grooveshark.com
Moreover the Flex layout manager is heads and shoulders above the box model madness of HTML/CSS.
It generally doesn't show up on mobile devices.
That's one valid point. But then again, how many AJAX apps can you name that are really useful on (which?) mobile devices without a special mobile version?
It takes forever to load.
Nonsense. http://omgpop.com feels quite zippy, no?
It disables UI conventions - like being able to right-click on the page - that users are used to.
Point taken. It replaces the browser context menu with a customizable flash menu. That sucks but it's hard to imagine how it could be done otherwise.
Hitting Ctrl-T when a Flash app has focus does not open a new tab.
Works fine here (OSX/Firefox).
It's not easily indexable by search engines.
Neither is AJAX content.
You may like it, but your users probably won't.
That depends very much on the application. Right tool for the job.