I don't think complexity always has to mean the fastest or the most time signature changes. It can be something that's simply more creative and throws something unexpected at you. And I think The Astonishing, for example, was great at this. You're listening to some cool, melodic rock tunes at first, and then Lord Nefaryus comes on, and it's a freaking tango beat. How many rock bands dabble in tango?
Then A Savior In The Square comes on, and aside from that progression from acoustic to heavy, you get to 3:21 and there's that choral bit, small as it may be, that immediately grabs attention. Point is, I think that kind of stuff is approached with the same mindset as anything fast and complex on their part.
But I never understood the criticism that DT (or that kind of stuff at all) is just for musicians and nerds. I mean, okay, maybe nerds in a sense that people who actively and passionately analyze things they like, but by that definition, everyone on earth is a nerd about SOMETHING. It may not be perfect for people who only listen to music passively, and only have enough attention span to enjoy simple, catchy hooks. But "not perfect" doesn't mean they wouldn't appreciate it. It's just a little foreign to them, and DT has plenty of catchier stuff to ease them into the idea, I think.
Kinda going off on a tangent there, but yeah, the bottom line is, I think technical skill fairly important for DT. Like the post above me says, their balance of the technical and the tasteful is precisely what sets them apart. They manage to find that balance, and not sacrifice either quality, and that's essentially what makes DT DT. If they abandoned their technical aspects, they'd still be a nice and pleasant band to listen to, but they'd be abandoning half of their identity. I don't agree that they did this with The Astonishing, but they did dial the complexity back a bit, and even then, people were already up in arms about the album, so yeah, clearly it's not an aspect that they could just take or leave.