For me, it depends on how you mean special. There are different kinds.
Inquisitor: Start with a special, important power
Warden: Only person willing and able, empowered by knowledge of what's really going on. Has ability to call on support.
Shepard: Starts only as "best of the best" but becomes special through the plot.
Hawke: Not special in any way.
The Warden way worked great. We weren't special in any obvious way, but were someone who stepped up to the plate and took on a difficult task because it needed doing. We didn't learn why being a Warden mattered until the end and it was delivered very well.
The Shepard way was also great, but for some reason, ME2 and ME3 abandoned it completely, except for one scene in ME3.
People don't seem to hot on the Inquisitor route, but I didn't play that game. I don't think I'm a huge fan of it, at least not for a series like Mass Effect.
Hawke was barely a protagonist. He didn't affect much and was more just buffeted around by the plot. No thanks. However, that was more a fault of the writing and not necessarily the idea of a non-special protagonist.
Hawke style really.
IF you think about it, Hawke was the everyman of these people; Hawke wasn't really marked for destiny like the Warden was, he didn't inherent a special place in the world like Shepard, who became the rival of the Repars.
Hawke was just there. Hawke did what they had to to survive, and to do the right thing in the situation given to them. Hawke was reactive because he had to react.
I think the Pathfinder should be the same way, reacting to the situations and them formulating their destiny as they go, rather than being marked for destiny as you say.
Not necessarily. They did so with Hawke, and truthfully it is probably their best written story thus far out of all of their games. The problem though is it was maybe too realistic for a lot of peoples tastes.
DA2 was also the worst story. Mass Effect keeps that Trilogy from being down there. Mass Effect 2 alone might be worse, but was also saved by it's superior characters and character arcs.
Shepard was too special by the end of ME3, I think it was ridiculous what happened... you can't put the fate of an entire galaxy in one person's hands and expect a good result. It's too much pressure.
Hawke is still one of my favourite protagonists because they were never anything special (except in the Legacy DLC) ... just someone making their way in the world, trying to survive and protect their loved ones.
The infamous hero's journey is an old hat, I really hope BioWare can come up with something better by now. It's not needed either. The PC doesn't have to be the child of a god, a former Sith or the last survivor of some special order... what's wrong with them "just" being an elite soldier? Sure, any other elite could do what they do... but does that matter if you are the one actually doing it?
Shepard actually wasn't special other than that he was simply there. They dumped what made Shepard special back in ME2 in favor of "he's an icon" which the plot never showed.
Hawke is also the most ineffectual and is simply caught in things going on around him that he really can't keep up with. That can make for an interesting story, but it's a rough sell for a game that we are engaging in as that protagonist.
As far as just being an elite soldier, that's fine to start, but I want something more. Either find or learn something important, like the Beacon visions from Mass Effect.