Iris was specifically given task to go on journey with Axew to raise it to powerful Haxorous. Something she stated herself and was confirmed through anime itself when touching subject of village of dragons and elder. Maybe it wasn't sole reason behind her adventure, but it made big part of it. Something which cannot be excluded when analyzing Iris career as whole, because failure to do that directly influenced her future path. Taking away from all previous build up about Iris talent in raising dragons when writers jut abandoned whole subplot halfway in her journey. Needless to say whole story about Drayden and preparing her to inherit gym loses a lot on its credibility and what will be if Iris future as dragon trainer when character itself showed zero interest in becoming Opelucid gym leader preferring rather to travel, explore new dragon types and seek for better, more reliable ways of mastering usage of dragon pokemon.
Taking any other route which confronts Iris desires would result in Misty situation number 2, in being forced to do something she does not really want to putting whole dragon master career in stagnation.
Considering how Drayden himself did not became dragon master solely by becoming gym leader, clearly having to prove his talent and worth to elders from dragon village and pass special tasks and exams evaluating his abilities. Which is expected from Iris herself to achieve as well.
But did we ever got explanation , concrete in depth analysis of how exactly Drayden became dragon master? Did we ever got proper build up and explanation behind Iris innate ability to read pokemon memories and feelings just by touching them(like it happened with Dragonite coming out of nowhere)?
Whole talk about Iris having to prove herself to village elders was only mentioned, but more palpable material and tasks, were they ever brought up and fleshed out?
Answer to all of this is No, so trying to describe Iris goal of being greatly explored and developed would be understatement to be honest.
Like i mentioned in previous post, Iris career had some merits to itself and was better described than its being given credit for. In knowing more about ending result and what whole title consists of than its case with some other characters who are in similar position.
I did not said Iris dream wasn't developed at all either. But it surely wasn't well developed resulting in lot of wasted potential, missed opportunities and poorly executed structure. Such as Iris mission of evolving Axew which went nowhere being forgotten. Unbelievable and contrived solutions to rough situations Iris found herself into, such as Axew learning outrage out of blue to defeat Luke Golett in club tournament just to witness that one time move never being showed afterwards. Or Axew learning giga impact on whim knocking champion Garchompon ground, being expected that viewers come to conclusion how Iris progressed ALOT until that point, when reality and amount of work invested in her storyline and development say otherwise .
Or tournaments and tasks dragon master in training is supposed to pass to obtain such title never being brought up and explained.
Did not helped either.
Than there is whole rivalry with Langley which ended completely unfinished going nowhere as well. And while Junior Cup followed by subsequent arcs was supposed to serve as arc to showcase Iris dealing with hardships on her own resolcing them through here own forces. Adding to her progression in coming out of everything as stronger, more experienced trainer.
Fact that Iris failed to do that not knowing how to deal with disobedient powerful dragons, with others having to play significant role in stopping Dragonite. in Ash defeating it with Krookodile decreasing its ego, Cynthia commenting on what was real issue behind Dragonite not following Iris commands(not having faith and confidence I its trainer deeming it as unworthy to be listened to).
Are taking away from ending result of Iris eventually earning Dragonite trust. Which by default was settled in very short period of time looking back.
When we fake in account how little it passed between catching Dragonite and Dragonite himself starting to listen more frequently to Iris. Regardless of occasionally still doing things on his own as it was showed in later duel vs Clair.
Writers also never touched problem others pointed out at iris, such as Georgia questioning Iris capabilities of becoming dragon master, with unusually small amount of dragon pokemon having on her hands. Or how in Junior Cup Iris coming to finals was nit due to her skills and merits as trainer but rather Dragonite. Who won several battles by himself making his trainer irrelevant through that period of time.
Issues canon brought up but were never exploited and developed in making Iris development feel more gradual and well rounded.
Likewise two wrongs don't make something right. Misty goal not being well exploited does not erase fact that Iris dream of becoming dragon master left A LOT more to be desired deserving better care and fleshing out than what we got instead. Especially when taking in account how much love and thought was put in May or Dawn for example development of careers respectively.
And on Misty behalf, mega evolution of Gyarados, having rich pool of water pokemon for water master in making, her goal of becoming water master being directly connected to E4 members or Whirl Cup tournament(and whole background about its relation to water masters) by themselves at least in logistic sense offered more concrete layout of what kind of tasks someone needs to overcome to become type master making visible progress through such acts. Than Iris dragon master career did.
Also Misty dreams not being adequately fleshed out can be excused due to being first poke girl with writers back than being a lot more inexperienced alongside production staff not being sure what they wanted from pokemon series to become. Than it became case with future girls. With writers by time BW started having enough knowledge and insight to make better use of potential Iris as character had than what was given in return. But than again in BW series it wasn't Iris only victim of poorly handled subplots and badly planned decisions. But almost all characters and continuity as whole for lot of various reasons as explained above.