You can have specific parts of the kit to be rigid and other parts of the kit to be more flexible. One doesn't take out the other. DRG is not the only job that needs to use specific attacks on hard CD so calling it brainless simply because there's a number of actions (perhaps there should be less) that are used on CD is misunderstanding the job imho. NIN is very similar to DRG in this sense, yet it's not considered brainless despite the fact that it has low positional thought, for instance.
No, it wouldn't push anything. Draconian Fire is still granted by the 5th GCD positional, this is purely an aesthetic change because I hate the animations of True Thrust and Doom Spike and because they are used only once in a fight. They're "dying" actions after level 76 and 82 respectively and it makes no sense to keep them when you can just give them the Leaden Fist treatment. In the opener, for instance, you'd get your first scale after the FnC, and then the 2nd one after the following WT just like usual. In fact, with a 3rd scale you could make it so that the scale is given directly by the 5th instead of the RT/DF. While this'd put the WWT under buffs in the opener, it may reduce flexibility down the timeline to put them under buffs though so it's probably better for scales to be granted by RT/DF.
The only change is that you gain 50 potency for every True Thrust you'd have used, so basically once in the opener and then one per downtime longer than X seconds.
You achieve the same thing by increasing the scale cap. If we want rewarding gameplay, then they should implement it in some way, but TT and DoS are old, outdated actions that should just be permanently replaced. We're already rewarded by our positionals due to how often they happen, but this doesn't mean other actions can't help with this. Being able to keep everything in strict CD is rewarding on its own as well.
This would save one oGCD, but other than that I don't see the benefit. My gripe with GSK is the fact that it can't be queued after Life, so LotD would have to either last 25s (but then it becomes more rigid to use your three NAS) or GSK to be a separate action, but then you wonder what's the point of it. I suppose that the best solution is to have GSK have no cooldown and an eye cost of two. However, MD must stay for increased flexibility or this change wouldn't really fix anything, but the opposite.
The fact that in full uptime scenarios you can just GSK > HJ and everything fits under buffs doesn't mean you always want to do it. There's plenty of encounters and situations in which you want to do HJ > GSK:
In P3S before adds, you do this to get an extra 1k potency on the boss with a double life before it leaves for the add phase.
In DSR, there's several phases in which you must do HJ asap or you'll lose an eye.
In P2S, you want to enter LotD before Kampeos and you switch the GSK/HJ order after the first arrows to make entering LotD more flexible for the rest of the fight due to the way buffs and HJ/GSK are unsynced from one another.
In dungeons, you want to do HJ > GSK so as to get as many eyes as possible and thus Life windows.
Even in full uptime scenarios, you may want to do HJ > GSK to get a double life at the end of the fight before the boss dies depending on the killtime.
Using HJ > GSK should never have any of them outside of buffs, it just means that one comes out before the other, and it's mostly done to get extra eyes and therefore LotD windows. Making it GSK > HJ by default will strip the job of a lot of flexibility, even if it wouldn't affect full uptime ST scenarios too much (but it still will).