There's just very little perceivable gravity to stuff that happens in these worlds, because the characters being focused on have little connection to it themselves. The drama is focused instead on what directly happens to them or, as the player, to you. The latter is where and why I think Mega Man X succeeded in telling a story: it was about you through the character, or vice versa. The games after that tried to get you to care about the overarching plot, which focused more on Zero and Sigma and less on X, i.e. you. Once X4 split "you" up, this culminated the shift of focus begun by X2. So, the plot involved both of them, but was more focused on Zero's importance to the plot; X became more an optional vehicle driving towards the unfolding of Zero's importance, in that he was the progenitor of the virus and Wily's last attempt to crush Dr. Light's creation(s). Take Zero out, and it's just X (you) and Sigma (or any other 'enemy'). The rest of the world remains a distant group of spectators.
With Mega Man Zero, you have more connections to the world in the form of Ciel and the resistance base, but even there I don't think the games do a good enough job of deepening those connections and making them meaningful. How much did you actually care about Ciel and the resistance base? You might like them, sure, but did you care whether or not they lived or died? Some of them were cute, like Allouette and old Andrew, while only a few (or one) actually helped you, like Cerveau and Ciel, but I never had a moment where I felt like my actions determined whether they lived or died. I never felt tense. The only exception I can think of is the boss fight with Aztec Falcon, but not only was that a pretty easy fight, but chances are you died before the garbage disposal shredded the Resistance members. While I can say Mega Man Zero is the darkest Mega Man has ever been, it's still more of an action game to me--and a hard one--than a dramatic experience.