This is an idea I’ve had for a bit now, and Missing Milo certainly didn’t dissuade me from it.
I’m pretty sure Dakota’s original timeline wasn’t very good.
Dakota only joined the time travel business to stop the Mississippi Purchase. That was it. His main goal was to stop this one event. Being put on pistachio duty doesn’t bother him because he did what he set out to accomplish. Why? What made it so important to him? Well, let’s look at him for a second.
Vinnie dresses comfortably. He’s the only time agent we’ve met who refuses any form of proper dress. He’s relaxed, and he eats as much as he can, when he can. What’re the odds he didn’t get to do that before he joined up? He was so excited to see Real Live Animals, which hints to the idea that he never got to do that before.
Despite all that, he’s no slacker. He knows how to fight, and immediately puts himself in front of Milo. He knows a back way to the Time Bureau, which Cavendish apparently doesn’t. IE- he makes sure to have a secondary exit at his own line of work. Dakota is always ready to run. Pretty much all of this is instinctual.
My bet is Dakota’s original timeline wasn’t the happiest or safest place, and the down spiral started with the Mississippi Purchase. Now that he’s fixed things, Dakota has found himself with the time and ability to just relax and chill and be happy, and he’s not taking a second for granted.
I mean, I feel you with the “Diogee is an OWCA agent” idea, but I prefer to believe that the OWCA are in awe of his level of self-taught skill and have been flooding him with job offers for years, all of which he has turned down in order to focus his energies on keeping Milo safe.