Alright, let's work off the assumption that it IS included.
Titan melee breakdown
Pros:
-Shoulder charge, one shot kill, and allows instantaneous directional movement.
-Barrier melee allows a robust over shield
Cons:
-Incredibly short ranged, t-Rex arms is a common monicker for Titans with respect to their melee. Warlock and hunter melees both win in range, and also have more practical modifiers. Sun singer gives an instant shield winning out most straight melee fights.
-force barrier requires the short ranged melee deliver the killing blow, making it unpractical and unreliable.
-storm fists modifiers offer little remarkable benefits
-shoulder charge requires a charge up time, and for any environmentally aware player, is easy to see coming.
-current shotgun/last word/thorn mets have ridiculous short range damage outputs, making charging players easy to dispatch
-the charge up time also means it isn't possible to use it on the fly, and most melee situations are spontaneous and unexpected. Therefore rendering shoulder charge impractical in most (I generously dare say 80%?) melee situations
-shoulder charge also has a short window during which it can be used, before requiring another charge up. (Thus the theoretical maximum fraction of time where you are "shoulder charge ready" is 5/8 of the time)
Overall balancing it out, Titan melees (right bumper and most situationally relevant) suffers greatly and is hands down the worst compared to the other classes.
Shoulder charge is a redeeming feature on striker Titans, but it's situational usefulness doesn't make up for the shortcomings of the more general use melee.
English
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titans melee range is much extended thanks to shoulder charge. shoulder charge will win a melee fight with a warlock thanks to the extended range and 1hko. you list alot of cons that are irrelevant. spamability. goes to the titan with shoulder charge. damage ouput, goes to the titan with shoulder charge. general benefits goes to the titan with shoulder charge thanks to the usefulness in movement and changing direction. range goes to the titan with shoulder charge. ease of use goes to the warlock. specific benefits goes to the warlock, mainly the shield on hit instead of kill. to me titan is the clear winner. not only does shoulder charge get them the best melee in the game they also have other melee's they can use. though you did pretty good listing the negatives of those, but they still have the other option.
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The problem with your argument is that your standard melee fight is NOT a charge of two players across a room in a dramatic clash where they both stand samurai scene style passed each other waiting for one to drop dead. Most melee fights are the result of spontaneous and unexpected encounters, where two players meet each other unprepared and close enough to where guns aren't a quick enough kill. Or as a finish in a close quarters fight. Shoulder charge just ISNT feasible in these situations since it requires prepreparation, and can't be summoned up in the few moments you have to act/react in that situation. And the standard Titan melee loses in that scenario most of the time. Shoulder charge is definitely deadly, and incredibly potent used right, but this makes up the minority of typical melee situations.
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shoulder charge just negates atleast some of those moments. of course its not usefull in the typical melee situations, but with shoulder charge you dont really need to engague in typical meee situations. its a ranged 1hko. I rarely come across someone in a room that I did not expect them to be in. the range and 1hko pretty much negates the standard melee fight as no other melees can kill someone in 1 shot. of course you can get shotgunned but so can anyone else trying to melee.