I am sure I am missing something that is good about it and I have my face palm ready for the answer to the question.

The reason I can't get my head around the new plot thing is that a lot of the cards that allow you to do it happen latter in the turn. I think the rookeries are all during the challenge phase. Why would a new plot be a good thing at this point in time? You wouldn't get more income. You could concievably up your claim by one, but why would I want to put a card like that in the deck. I am just not seeing how a new plot is doing great things for me. I can tell that someone thinks it is a great thing because of the cost associated with the card and using the ability but I am obviously missing something.

well i'm not so sure it is a good thing, i think its just a thing. That said i'm sure combo players out there (dobbler, paging dobbler) like it to do some funky stuff with it.

The things i've thought of with it are to reveal valar, then switch to a plot with actual claim value. or play a high gold plot then switch to a high claim plot. Or maybe once the new CITY plots get more invloved play a second city plot that phase (since they get stronger the more you have in the used plot pile) like city of shadows for the free shadows card and then city of sin for the kneel in challenge phase.

Lars is right that it is more of a "thing" and it is up to the player to do anything they like with it.

Mostly, though, you're looking at plot effects. Sometimes it is nice to switch plot effects during the challenge phase for one reason or another. There are certain strategic points, like the switch from a reset/control plot that you needed in the Plot phase to something a bit more useful in the Challenge phase that Lars mentioned.

There is a broader view that is possible to take, too. Have you ever played a plot in Round 1 or 2 and then, in round 4 or 5, you're really thinking "man, I wish I could use THAT plot right now..."? Revealing a new plot with Bran, the Rookeries or whatever does that for you, too. By cycling through your plot deck faster than your opponent, you may have more plot-based options than your opponent and be in a better position to leverage them.

I've got a Summer NightWatch/Maester-Martell deck build around this principle, it's a huge advantage that you can get through your plot deck faster then your opponents. Even if you used it only once, the 7th turn you'll have acces to 6 of your plots while they have to choose their last. It also lets you skip having only 1 option for plot.

One of my favorites to reveal later on in a turn is Snowed under, if you played it in the plot phase most people will leave their strongest units standing(and you've got 3g and 1 initiative). But if you reveal it during dominance (with vayle rockery) you might have some juicy targets to return to your opponents hand.

Golden tooth mine also works great in this deck(combined with summer and some other draw I often hit the 3card cap)

Revealing a valar morghulis after you did your challenges but before your opponents could begin theirs is always nice to, the 0 claim doesn't bother you then.

My deck can get valar morghulis quickly and since it has quite a few saves it's very resilient against it. I can get board dominance real quicky and keep it up while I replenish my hand rapidly.

All very good ideas. I am leaning towards it is just a thing right now, but the revealing snowed under during the challenges sounds nifty not game breaking but pretty cool. Also Valar after you have made your challenges but before the get to is also pretty devilish.