I know it doesn't reflect well on me that I'm yearning for a middle manager / foreman to delegate things to in a game I play.
But really, it'd be nice to very slowly reap the benefits of professions without all the fussing over them.
Me flipping between menus, and sometimes going back and forth to the auction house to get the materials, really drives home that this part of the game involves neither dungeons nor dragons, and starts to get to the "spreadsheets... in... spaaaace!" model of other games. I'd prefer to aim my grinding at other parts of the game, not things that don't have me even moving my character around onscreen.
I'm sure Cryptic could balance what a Taskmaster could do for you in such a way that opting to go that route lets it slowly churn in the background, yet someone who knows what they're doing could really squeeze a lot more out of it. Like, Taskmaster will only ever assign the highest-ranking worker possible to a task, and only one of them at that... if you want to get bonuses for assigning additional workers you need to do it by hand.
Taskmaster could be set to some really simple directions, like "progress these professions, in this order, with the resources available". So e.g. if you have the resources to do a task that generates more professions XP for that professions it will do that first... if not, it will do whatever it can afford, like the highest-XP resource gathering.
There could also then be an option where Taskmaster can present some options, e.g. "if you let me go to market to get X resources, I can do Y professions tasks for you and progress that much faster", and the cost of X resources would be same as the default market rates that the game presents to you in the auction house. Taskmaster would then go find the auction that has closest to but not over that amount, for exactly that number of resources (no automated purchases of say a stack of 99 or something). If it couldn't find that exact number you'd need to reach in to buy manually.
Taskmaster could be developed out of the Leadership track, and cost some amount of AD to do your professions for you. It'd be a daily thing to check in on, like VIP rewards.
Perhaps a high enough level guild would let Taskmaster draw from guild resources, and/or be paid in guild marks instead of AD.