This sounds more like a complete system overall rather than a Quality of Life Suggestion. What you're wanting is to completely scrap the way loot currently works.
Square Enix don't want a divide between hardcore and casual players, they want them to be on an even playing field which is why we have a ridiculous lock out system currently. (Ironically it doesn't benefit anyone actually)
Already said they're doing this.
This also crossed my mind once, it'd be rather handy.
Can't really compensate for human-error and stupidity here, its a simple as waiting and not leaving.
They're already adding in a refresh version of the party-finder in the next update (or 2.2) which will allow it to notify you if the duty you're seeking is looking for [X]. Every 5-10 seconds however would put a HUGE strain on the servers having to populate the list every 5-10 seconds for everyone, whereas currently there's less stress with the vast majority of people not pressing the party finder button every 5 seconds.
This would lead to the issue of "We never see any Dragoon loot, but this fight requires that we only take ranged DPS!"
The way this game is set-up is, not every job is used for every fight causing major loot pool issues if you only got based on your party composition.
If you're talking about pre-made parties, this would cause huge issues and it's easily fixed by simply removing the person from your party and entering again.
A lot of players use it as a "ready-check" feature to see if everyone is there, this would cause huge issues.
# Queue for Garuda Ex
# WHM is AFK
# Duty Finder Pops they don't accept, kicked them immediatley and puts a duty findered healer into the party
# Your party enters completley confused by the fact your healer has now been replaced with someone completley random, wondering "This is the most ridiculous system ever, wtf"