That's not why Romeo and Juliet is a tragedy. It's a tragedy because their families are so blinded by hate for each other that it leads to two innocent (yes, impulsive, but innocent—especially for the time of writing and the literary and stage conventions of the age, nothing Romeo does would be considered creepy or weird) teenagers losing their lives because the adults around them make them think they have no alternative and no future just because they love each other. Act V, scene 3 (specifically the part where Prince Escalus chastises Capulet and Montague) makes this pretty explicit ("See what a scourge is laid upon your hate, / That Heaven finds means to kill your joys with love!") and blames them for Romeo and Juliet's death. West Side Story (an adaptation) makes this even more explicit by having Maria, the Juliet character, survive and blame the rival gangs for killing Tony (Romeo).