About your question "Do you really need Yii?"…
Well, there are just a few things people actually "need".
For all other things is a matter of "want" or "like".
Do we need Yii? Maybe not.
We want to improve the PHP side of the house for sure.
That would mean having a good framework, improving tests, migrating to TDD, etc.
We have several options for that.
The true is that in the technology field there are lots of choices to make.
You can do everything on the database or almost everything on the application side (1), among a lot of other options you have.
The discussion about the pros and cons of each options is too big for this message but you get the point.
The problem is that when we are good with the hammer we tend to think that every problem is a nail.
There is no best solution for any problem.
It depends on the nature of the problem and the people working on it. Mostly on the people.
Finally, where is the web-development going?
Tricky question, isn’t it?
Personally I see a few milestones on the web-development field (of course this is also a huge topic to discuss here).
First Javascript libraries. The are playing a big role on enabling better user experience on the client side.
Firefox as a development tool helped too.
The Javascript framework you mention is related to this. There will be more projects like this, essentially expanding the jQuery-UI project.
One of the biggest changes (not so new but extremely popular now) is AJAX. That changed the way the browser is used as a client agent.
What to do client-side and what to do server-side is (2) a design desition that a developer has to make.
One side (client) will not replace the other (server) (3) or viceversa.
JMG
(1) I consider this a biased term. The database is the application side too! 
(2) This was always a desition to make, this is not new. But as the client side becomes more complex, more is handled by the user agent than before.
(3) Who will create that JSON data for the client anyway? 