until maybe a year ago, we talked about optimazion for the user, due to slow internet connections. Now We hardly care anymore, as internet connections improved a lot.[/quote]
This is true in many places in the world, especially in the cities and suburbs of first-world countries. But not in rural areas, and some emerging internet markets. In many areas, mobile users have limited cellular bandwidth when away from "home". Even if they can find a 3G or better cell. In some locations, wifi-only users are limited to "internet cafes" and other semi-public venues (stores, RV parks, marinas, hospitals) with slow wifi or just too many people trying to use the wifi bandwidth at once. Think of the kind of bandwidth that was available to "Arab Spring" users attempting to create internet hotspots using tools designed just for that purpose. And think of people trying to use a forum and also trying to avoid over-running their cellular data plan at the end of the month.
Many forum owners still need to consider the load this kind of thing places on the server as well as on the user's internet connection.
If AJAX can be used to put up needed new information without imposing an entire page re-load on the server, user, and internet connection -- so much the better.
Where AJAX winds up being used to make "more cool stuff", like shoutboxes that poll every second from every open window open to the forum everywhere in the world, it will be a problem for some forums and users.
It is still a matter of what it is used for, and how it is used.
That said, some of what the user suggests is doable just in JS, without AJAX at all.
Form validation can be "interactive" not requiring the user to hit the submit button (or even disabling the submit button until the user fixes the data). That would improve "flow". "enter the password again" comparison can be done as soon as the user fills the second field.
In some cases, using multi-tabbed forms for admin settings MIGHT make sense, for some forms, avoiding extra page loads. It might also lead to users switching between forms and not saving changes, unless it were implemented very carefully.
It could also mean re-arranging the forms, so that things that logically belong together will be found together, instead of (or in addition to) on the forms they have historically be on for the last 7 years. SMF 2.0 has some more complicated options than 1.x has, and that means a little re-thinking might be in order as we move on into future SMF versions. This is more about design focussed on usability, and may have nothing to do with page loads per se.