With all due respect, I'm afraid that the issue of genre has been left out altogether. Romeo and Juliet was meant to be a tragedy. It has often been said that it does not rank among Shakespeare's best works. However, it would have been an anticlimax to "kill" the protagonists on such a petty pretext as impatience.
The play announces from the very beginning that it deals with "a pair of star-crossed lovers." Therefore there must be a sequence of events that leads to their untimely death. One could think of the tragic outcome from a fatalistic viewpoint -i.e., the couple will die regardless of what they do or not do- or from the point of view of causality -a sequence of prior events that, taken together, lead to the only possible ending.
I find that both fatalism and causality intermingle in Romeo and Juliet. It is a long chain of "ifs" beginning with their families' ancient enmity and ending with a reversed "comedy of errors." What we have here is a "tragedy of errors." The lovers died because of the misjudgments of those who should have protected them and because of their own lack of judgement.
In our times, we think that such young people are immature. Still, in Elizabethan times, with a much shorter life expectancy, life moved at a much faster pace. It would be at least shallow on our part to attribute the couple's death to only one factor. We need to follow the chain of events that their deaths closed. We also need to remember Mercutio's words as he lay dying: "A curse on both your houses." Bearing in mind the superstitious nature of the age, we can add an extra element to our speculations on the subject.
Consider that during this time period they would not have been considered impatient. After all, Juliet's father was willing to marry her to Paris, a man she had only met once. Marriage was the only way for a woman to support herself. Men would have been expected to find a wife and settle down quickly (past a certain age of course). While today many people date for years before they marry, this was not the case in Shakespeare's time. Couples married quickly. Romeo and Juliet would have rushed to marry when they found a possible partner. Many of today's readers consider Romeo and Juliet to be hasty and impatient, but they would not have been seen in the same light in Elizabethan times.
You could argue that it was bad advice that got them killed. If you're not supposed to say that it was impatience, then blame it on Friar Lawrence. Blame it on his silly scheme. Or blame it on Malvolio and Tybalt. If Tybalt weren't so hotheaded, Romeo wouldn't have killed him.