Regarding fighter damage output, right now a fighter that is doing MT duties is using 3 different sets of cooldowns, all of which have damage or damage+threat, bolded items require vengeance:
[Feint | Frenzy] , [Rend] , [Shield Bash]
A fighter that isn't doing main tanking is really running two sets of damage output cooldowns
[Feint] , [Cross Cut]
In theory, moving from a tanking posture to a dps posture, you'd lose the damage output of frenzy, and the damage output of shield bash. This lack of damage output from abilities, in theory, should be somewhat made up for with cross cut (whose damage is supposed to be greater than Rend) and offensive stance (increasing all damage output) dual wielding. In practicality, I'm not sure how many tanking fighters are getting high levels of frenzy off. This problem is a known (at least to the fighter community) issue with vengeance that has been talked about a ton. I wouldn't be surprised if a tanking fighter and a non-tanking fighter are actually outputting similar damage over any fight in the group-level content.
While fighters do melee dps, that's more of an explanation of what they do rather than an identity of the class. Fighters have received an increase in utility, probably because of people complaining that fighters had no utility, that only modestly allows them to contribute more than before in a group setting with Kneebreaker. A fighter that isn't doing main tanking is bringing Feint and Cross Cut, and also a potential snare in Kneebreaker, AC debuff in Armor Break, physical damage reduction in Unnerving Shout ... all things that aren't on the bar if you're a main tank for a group or a raid. I'll leave Vanguard out of it now, as it's been updated to a longer duration, but that's increased utility (in general) for the fighter. I'm not commenting on whether I think this is good or not, I believe my position on where fighters are right now is abundantly clear. I bring this up because it might be worth accepting (as a group) that while it says "melee dps" on the class page, that means something very different to the devs than it does to us, the players.
I'm not sure if there will ever be a good answer to "will a group with a tank take another fighter?" I'm not sure it will ever be in the optimal interest of a group to take a second tank. Flip the question around, would a group with a Fighter take a Paladin? or an Inquisitor? Or a SK? Generally, no. For the same reason that, generally, they won't take a second healer. All we can do, as part of the community, is not play that min-max game when we are empowered to do so.