No. Simply because weapons shouldn't be locked to a class. I had the same complaint about the class exotics you get from the gunsmith.
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What they should have done was have the quests be tied to a specific class, let the other classes be able to use the weapons, but have the special perks only work for the weapon's designated class. For example, ace of spades is unlocked by playing as the hunter and can use it on my Titan and warlock, but have the exotic perk maverick locked out of those two classes and leave the perk exclusive to hunters. Same goes for tlaloc and fabian strategy.
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I don't agree about the perk. I was all for the quest needing to be don't a particular class but once you finished it all of your characters should be able to use the weapon you got.
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There should still be some exclusion to the classes. Why would warlocks and Titans get full advantage of the weapon that hunters worked hard for?
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Because it's all the same player. Because it is still the same account. The same logic could be asked of why after all my efforts can't my warlock use the handcanon I earned on my Hunter? The player earns them so locking them by class is stupid. Sure the quest should have to require the class but once I've earned it let me hand a weapon to any character.