Tybalt is portrayed as a villain in the play, and yet his death is not a positive event. Why is Tybalt's death bad for Romeo and Juliet?

Well ... Tybalt is Juliet's cousin. Although he is mischievous and a bit of a rogue, he is still well-loved by Juliet and the rest of her family (the entire Caulet clan).

Romeo is now a murderer (forcing him into a rapid departure), and a murderer of a member of Juliet's family to boot! If things weren't already against him in blood alone, this act would certainly sour any advancements he could have possibly made in asking Juliet's father for her had in marriage.