Gaia's hammer was actually a mistake made by Tetsuya Nomura who was unaware there wasn't a hammer-wielding already in the game, but Yoshi just laughed and kept it in anyway for the 'coolness factor'. Besides, NPCs are a poor indication of new classes because since day 1 of 1.0 they've had access to weapons and skills that players have never been given (like Rostnsthal dual wielding a pistol in one hand and a single handed axe in the other, simply because it's 'cool').
Time Mage's role and abilities are already taken by AST anyway (AST has, or had, a lot of abilities that dealt with manipualting time and space, like Lightspeed being effectively Haste), so AST is really just Time Mage under a different name. Hence it would be rather redundant to include an actual Time Mage at this point (to say nothing of back during the Beta Yoshi all but ruled out an actual Time Mage by saying he thinks spells like Haste would make the game "too easy").
Your initial idea for Jester basically is an evasion tank that players made NIN into in FFXI, and that was all very well and good, except they abused it for it was worth, and once their shadows went down they were torn to pieces (and SE increasinly made enemies capable of tearing through NIN shadows with ease just to muck up these players). It sounds good on paper but in practice is a nightmare for healers.
The second idea you had for Jester sounds too mechanically complex for SE to bother with, to say nothing of being too overpowered as it pretty much could satisfy any duty requirement without restriction, practically invalidating the role of every other Job. There is a reason the Crystal Exarch has this very role adaptability in the Trust System during Holminster Switch and that was simply because there was no other story character available to be used in Trusts in that part of the storyline (the only dedicated tank in the Trust system, Thancred, doesn't appear til much later) and so he is an exception rather than a rule.
Also throwing knives are already a ROG/NIN ability so this is already taken by an existing class.
Bloodmage is pretty much what THM was like in the original launch version of FFXIV (version 1.0). There, THM did not have Fire, Ice and Lightning spells (those were CNJ spells). Instead, THM's original gimmick was using drain spells to steal enemy HP to replenish their own or their party's, while also having access to debuff spells and even Light and Darkness elemental spells like Dia. This was all scrapped when the Jobs were added in a patch and the classes were redesigned to make them more appropriate for their Jobs - hence THM was radically altered, probably the class given the greatest makeover in the game. They lost the drain healing, with CNJ becoming the dedicated healer class, and gained instead Fire, Ice and Lightning spells so it could be a better fit for BLM, retaining only the Astral/Umbral aspect as a focus shift mechanic.
As THM has never regained those abilities it's lost, it's pretty clear SE considers the original form a failed idea and so I do not seem them reviving it I'm sorry to say.