I feel as though SE won't do this simply because JAs cost no MP nor ammunition to use, they need to have some kind of delay. Magic has a delay and so do weapon skills. DNC isn't a mage per se but its steps/waltzes and flourishes are instant cures/buffs/debuffs. The delay on PUP or DNC abilities serves as an analogue to mages. Mages use magic, which has delay, and light armored jobs use JAs for special effects/bonuses which are given a delay as well. It's a balanced mechanic I think.

Take waltz for example. It has a delay that interrupts your attacks and prevent melee swings but it cant be interrupted, it can be cast while running, it's instant and can't be silenced. Steps lower def or evasion, they can miss but they don't expend tools or MP, they expend TP which is technically 'free'(no refresh needed etc).

Manuevers allow a PUP to use their pet's abilities which is the main aspect of their job, they're not Monks so DDing on the master isn't 100% of their job, half of their job is the Automaton which is how SE justifies the delay. I feel like SE lets the JA delay slide on these jobs since from their original vision sees these jobs as support damage dealers not main frontline damage dealers like SAM WAR MNK DRK. DNC and PUP fit that ambiguous,tactical, light armored, rogue archetype. Moderate damage but has a host of gimmicks or special effects that enhance the party or debuffs the mob, but could concentrate solely on damage if need be(to a lesser extent than a main DD job though). I think if you look at PUP how SE envisioned them and less how you want them to be played, it makes more sense. DNC and PUP are so versatile and can do so much more than a SAM WAR MNK DRK(in terms of roles i.e healing, debuffing, nuking) that the JA delay in a way creates a barrier, preventing them from entering the realm of those SAM WAR MNK DRK jobs which can't drop a waltz or a fire V and can only output damage. Because of that, the JA delay is an indirect barrier preventing jobs that have high damage potential but also have other tools and versatile abilities that main DDs dont have, from becoming overpowered.

tl;dr DNC swings extremely fast, has Cure V and Cure VI, debuffs, has a 10% haste JA, great SC ability, reverse flourish and a ton of other JAs, 2h DDs have way less than that; so the JA delay kind of prevents jobs like DNC from becoming too powerful; besides mages have cast delay way longer than JA delay