I just wanted to add this because I did not see any of the answers.
The reasons for using Ajax are mostly about the controls that you get a lot. These reasons were mentioned above.
One major flaw in Ajax, however, is that it is a JS fix. JavaScript is a great language, but people have been throwing it at every problem for a while, and everything that can be optimized if they were built into browsers now runs slowly (compared to compiled languages) with JS.
iFrames is a great example of this. They represent an incredibly common use case, wanting to include some html in some other html. Unfortunately, they are not very surprising at this, often creating more headaches than anything else.
If you want to include something and not have a mess with it on your site, as well as your site to mess with it, iFrames are great. For the more common case of using some random html in some other html, Ajax is better.
And here is what I'm trying to do: it's stupid. There is no reason that there shouldn't be something like an iFrame that looks more like Ajax. But, jumping on board (like all of us) with Ajax, we now have no choice.
The biggest reason this is a problem is because JS should never have been the absolute building block of the Internet. In addition, it is used on almost every site to violate user privacy. So, if you are looking for a good reason to use iFrames, this is mine:
Feels good, no need JS. If you can improve your site with JS, and not dependent , then this is a hard-earned achievement, and the site will feel less “hacked" in general.
In any case, this is just my input.