Although I only just dabbled in turn based today, I have a feeling that people are probably underestimating the value of initiative.
I think it's interesting to compare Darkest Dungeon and Divinity: Original Sin here. I played through most of DOS, and there initiative didn't feel like it mattered that much. I think this is because, from what I remember, the same strategy tended to work in every fight, and you could just kind of bulldoze every fight without much thought. On the other hand, initiative in Darkest Dungeon was crucial, because so much was determined by what happened in the first couple rounds of a fight.
When done right, initiative is ultimately about the ability to control combat. People are already figuring this out for avoiding interrupts and grabbing engagement, but there's more to it still. In general, for any debuffs which hamper the combat ability of your enemies, you want those hitting before they get a chance to act. Although a high initiative may translate to just one more round, that first round can have a ripple effect through the rest of combat. Done right, and your opponents never build momentum. Conversely, by acting before enemy debuffers, you're avoiding one extra round of debuffing, and just as importantly, you're avoiding it now as opposed to later.
I think it's going to be hard to say where Deadfire lies on the DD to DOS axis (that's a lot of Ds), but I'm hoping (and suspecting) that it's closer to the former than the later (and fwiw, I loved DD and more or less hated DOS by the end of it).