I think the issue with Outtrigger, from the brief demo I played it of on a demo disc I collected, was the controls. In a time before dual analog sticks were the future for console FPS, Outtrigger had to make do with a clunky, not exactly accurate or precise method of control. That and the fact that mono-analog FPS controls have you doing things reverse to the standard of today to get optimal results is a hard sell (though I don't know if Outtrigger supported such a control scheme). Of course, all this could be fixed with a remaster, but would SEGA bother? Outtrigger is kind of generic in everything but gameplay, and even then, it wasn't too dissimilar from shooters of its day. Maybe more arcadey, but still.
I will echo that I would love to see a SEGA take on the FPS genre again. We've got plenty of third person shooters from them; Vanquish, Binary Domain, Border Break, but the only FPS that immediately springs to mind is Condemned, which is more of a horror beat-em-up in practice.