No they couldn't. Monk pulled from Lancer and Marauder. Dragoon pulled from Pugilist and Marauder. The only jobs that could cross Gladiator were Warrior and Dark Knight.
Classes could pull from all, but then, as a Monk, you lost Fists of Fire and Dragon Kick.
However, it was never a viable option for Dragoon or Monk to tank as you lost more by not having a tank than trying to replace it with a DPS. We have to remember that whilst Skull Sunder did generate enmity, it was uncomboed and was only 100 potency.
However, going back to the main point, if you were to extend cross class actions to job actions, what would you actually pull? The vast majority of damage actions are ingrained into the rotation and wouldn't work outside it. You could just cross the buffs (Riddle of Fire, Lance Charge etc.) but then you are just stacking buffs. That is hardly changing your rotation or adding anything interesting.
Again, it is one thing to just say, well, they could do it/make it better, it is another thing to actually do it and do it right.
On the topic of Blue Mage, do you actually have a choice, or is there a standard set of Blue Magick for each role that everyone just copies?
As for Bozja/DR, even IF people interacted with the essence system, they used it to enhance their DPS and in general, if you went in as a role, you stayed in that role. It was only in more exceptional circumstances that you 'swapped' Have way too many healers, you agreed on who was the healer healer and who had the 2 button DPS rotation. The only other instance I had personally seen (bearing in mind I completed all of the ShB relics in the expansion, so I done a lot of DR) was when there was not a single tank in the whole instance and I tanked it as a Monk, of which I luckily had the essences to do so. Now imagine if noone had that, it would have been a dead run before we even started. Which ties nicely back to cross class and tanks not having Provoke because they didn't level Gladiator enough (Provoke was level 22 iirc, so you didn't automatically get it just by levelling it to 15, not that DRK needed to level Gladiator at all). You COULD do the dance of managing enmity without it, but that comes with it's own issues, not least of all PLD n both ARR and HW had enmity boosters in their damage rotations (however, the issues come more from information display than anything else).
There are a lot of issues that hide below the surface which is why I always say you have to think critically about what you actually want and what the pros and cons are. Do the pros outweigh the cons.
Character progression was putting stat points into your main stat. Yay. Could it be expanded to put them into secondary stats? Sure, now they all go into crit. If you have a different idea, please share.
Gear progression, there is going to be a BiS, no matter if it is for every fight, or specific fights, or hypothetical different builds. What do you actually want to see out of gear progression?
What systems are you actually saying they should add? Taking into account how players actually interact with said systems and not necessarily how you want them to interact.