I like the theory that operas actually need their relatively melodramatic plots. It's the nature of the medium to heighten emotions, and nothing inspires (or tempts) a composer more than some extreme situation calling for the expression of intense feelings (you don't see many operas written about, for example, accountants doing an audit). It's not so much a flaw in operas, I think, as it is an element that helps them break through to a dramatic level few other art forms can touch. If Violetta in Verdi's "La Traviata" or Mimi in Puccini's "La Boheme" both have to die for their beloved after years of suffering and heartbreak, that's not some silly convention you have to endure again and again but a meticulously prepared and carefully timed moment allowing the composer to pour his heart out; and, far as I know, an outpouring from a Puccini or a Verdi is all the excuse you'll ever need to listen.
The problem of "Rent" onstage, I imagine (I haven't seen it onstage), is that it's Puccini's premise without the music (okay, Puccini took his scenario from Henri Murger's "Scénes de la Vie de Bohéme"). One thing (maybe the only thing) that justifies Jonathan Larson's modern-day Manhattan version (it's set in Alphabet City, a rough neighborhood that has recently seen a surge in upscale housing) is the introduction of AIDS. Talk about upping the ante from Puccini--not only is the heroine dying, but half the cast and a good number of bystanders as well (this was in 1996, years after Norman Rene and Craig Lucas' film "Longtime Companion," our own Laurice Guillen's "The Dolzura Cortez Story," and Tony Kushner's epic play "Angels in America" dealt with the subject in their own more thorough and more profound ways).