Golden Girl

It might - just as long as they add Incarnate mobs to streep sweep and repeatable Incarnate contacts to it - otherwise, there's going to be a stampede to DA by everyone interested in Incarnates
There's zero reason to gather in PD or the RWZ when DA offers Incarnate rewards in the downtime between Trials - DA's going to be the Trial staging ground that quite a few people were asking for when the Trials first came out.

A low population in the only zone in the game with Incarnate content?

Looking at the top of the forums for the market items once a week doesn't really take a lot of time

They'll be the minority

People will be in DA for one reason - Incarnate content - the chances of smaller groups of them deciding to join up to get faster Incarnate progress on a Trial are pretty good.

You misread - the thing that's not really meant to be done much is unlocking every single tree in every single slot.
Basically, what the Incarnate system is, is something that a few people have suggested before for the rest of the game - a free-form power selection method.
Only instead of the notmal framework of a free-form power selection method, where you can pick any type of power, but only a certain number of powers in total, the devs have given us the option of taking every single Incarnate power - with the only restriction being the time it takes to actually craft them.
Unlike the 1-50 part of the game, where your powers are limited in number and in theme, based on the choices you made at level 1, the Incarnate system allows anyone to take anything, with no limit except the crafting time.
If you choose to paly, say, a fire based avatar, then the game will offer you a selection of new fire based powers as you level 1-50 - but when you get to the Incarnate system, you aren't limited to fire based Incarnate powers - you're given a choice of every single Incarnate power - but that doesn't mean that you're supposed to have every single Incarnate power.
Right now, there are 5 slots, but 42 different power tress - the system is not designed for it to be normal to unlock 42 T4s, or even 42 T3s - an average Incarnate will have 5 T3s, one for each slot, giving them close to the best of each of the 5 powers they've chosen, and the 3 level shifts - T4s are more for those players who want to squeeze every last bit of perfromance out of their avatars, as the bonus from T3 to T4 isn't very big.

It's a no brainer - if there's a team of 8 doing one story arc, and a team of 6 doing another, it only needs one click of "invite team to league" and they're ready to go for Lambda - and the LFG working while on missions makes it every easier.
And when there's a choice between hanging around chatting on the RWZ or Pocket D between Trials, or spending that time street sweeping in DA and/or running the repeatable Incarnate contact missions, with the added bonus of being able to use the LFG while you're on a mission, then there's really no reason why anyone wouldn't go to DA to form a Trial.

Peregrine Island got pretty quiet once the AE came out

The slower progress rate means that the DA content will be useful as a filler for the downtime between Trials - DA will become the main raid zone, instead of the RWZ and Pocket D, and leagues will be easier and faster to form in DA

There are hundreds of Warworks and DF to mow down on the Trials

There's a solution to the problem in the second half of your sentence

The Alpha slot is a very good intro to the Incarnate system, but it has limited potential for further progress, as there needs to be more challenging content for us as we get more powerful - the old non-Incarnate content doesn't offer a challenge to an Incarnate.

You don't need anywhere near 100 Trials to get to T4 in the 5 slots
Or do you mean getting to T4 on every tree for every slot? Because that's not really meant to be something many people would do

But then they'd be advancing on content that they were too powerful for.

If there were no rewards on the ITF, would it still be run as often as it is now? Or would it become "annoying"?

They're not realeasing that much new content each week

But you're still repeating content - that's why it seems weird to want non-repeating content now, when you've been repeating content since hte game began.
No MMO developer can produce content fatser than their players can play it - so making anything that's non-repeatable is just crazy.

The problem with that attitude can be seen in the AE - the devs discovered that there is a section of the player base that will zero in on the quickest path to progress, and ignore everything else - it wasn't a majority, but it was big enough and done frequetly enough to get the devs to make so many tweaks to the AE, including aded Marty to try and slow them down.
Because this section of the player base was just door sitting on the same AE farms 1-50, that could be interpreted as the rest of the content "sucking" compared to the AE farms, because they were only doing the "fun" content.

Repeating content?

I can type fast

You're not losing anything - the current version of Dark Astoria will be kept as an echo zone - everything you like about the old zone will still be there for you to access.