Well, let's see. Tragically missing parents, hunted by cops, sounds like Batman. "No, no, no. This is the new 'grim and gritty' Spider-Man with the mysterious past who is driven by the deep secrets of his childhood and equipped to handle the modern world!" Haven't we seen this before? Oh, yeah! Batman!
The reason that Batman has lasted as long as it has is because of the simplistic motivation behind the character: revenge melded with a personal sense of 'justice'. The reason that Marvel took over the comic industry in the 60s and has never relinquished it is because their characters were originally driven by motivations far less Gothic or nebulous in tone. Spider-Man, for example, was driven by guilt and a sense of personal responsibility. We've all been there. Very few of us have been motivated by revenge as the driving force of our lives. In fact, it's hard to see how long that could drive anyone, which is why it's more difficult for people to relate to Batman for lengthy periods. He becomes the antagonist of his own books, because it's easier for people to relate to his wacky villains and their often quite human instabilities than the granite-like icon of justice. Spider-Man is, in many ways, Average Joe and is motivated by the same things that Joe feels or has felt. That's what makes him work. Turning him into Batman is at least mildly pointless and certainly won't give the script writers any more room to maneuver; often less. Severe caveat here: I haven't read a Spider-Man book in almost 20 years, so the current character may be a refugee from Bamboozilonia, for all I know. I do know that the character's long-time marriage was ended some time ago by one of Marvel's facsimiles of Satan, Mephisto, in true Bobby Ewing fashion, so it's not like Marvel has been completely immune to the Hollywood (or DC, for that matter) impulse.
I guess the question comes down to: a) what makes a viable, long-term character? and, b) is it possible to have a story without an ending? Looking at a), there are often external constraints, especially in the world of film, that prevent going forward with an established franchise. There are reports that the main actors of the Raimi films no longer wanted to participate. Given things like the dancing scene from Spider-Man 3
it's hard to blame them. But it's also true that often what is most compelling about many superheroes (or heroes, in general) is their origin story: the foundation for why they became what they are and act as they do. In most cases, this is Joseph Campbell's "hero's journey" in some form or fashion. However, I think the secret to Marvel's success with characters like Spider-Man (and the long-term affection that enables extravaganzas like a multi-film buildup to tonight's Avengers) was in breaking away from the "tragic circumstances" motivation and continuing to present the characters as actual people, with bills, family, school, work, and all the other facets of modern life that most of us deal with on a regular basis.
When Spider-Man first emerged in 1962, he was presented as a teenaged nerd getting his first real taste of power and admiration, only to let that go to his head and find that a simple lack of action on his part contributed to the death of one of his guardians. The now-canonical catchphrase: "With great power comes great responsibility." became the foundation of his willingness to run around in blue-and-red tights and risk his life on a regular basis. When Marvel discovered that the bulk of their readership was no longer 12-year-old boys but, in fact, college-aged men with money to spend, they did an unfathomable thing in the comics world: they let their characters age. Peter Parker was now a college student, in addition to his part-time job as a photographer. The character was instantly relevant to its primary audience. The aging process slowed down a bit (otherwise, we'd now be talking about The Amazing Septuagenarian) but an effort was maintained into the 1980s to continue to present Spider-Man as that same Average Joe, which was replicated by Sam Raimi in his trio of films. Is that somehow not sustainable at this point? Has the character become too long-term, as it were, to continue to be viable?
In the comics world, the answer would almost invariably be "yes". Comics, as a serial periodical, suffer from b): The Story That Never Ends. You don't get real conclusions. You get temporary cessations of story arcs. The further challenge is that each comic, if properly written, has to have that same beginning, middle, and end to maintain a narrative flow from month to month. Jim Shooter, long-time editor in the comics world, used to say that every issue was someone's first read of that title. So, it had to be accessible to new readers at the same time that it maintained enough complexity for regular readers. TV functioned under the same constraints for decades, in that most dramas or comedies had to present a scenario that a new viewer could engage, but also have enough regular aspects in the form of returning characters and their idiosyncrasies. Thus, each week became Gilligan or Captain Frank Furillo running into variations on a dramatic theme. Most TV series eventually get cancelled as a consequence, since the story simply can't maintain itself with any kind of integrity. The most notable exception in recent years has been The Simpsons which, as a cartoon, is a lot like the comic world: the physical constraints of actors aging has little effect and the story isn't burdened by having to give each character screen time or pay them to sit in their trailer.
Furthermore, The Simpsons, free from those physical constraints, can become far more of a marketing tool. Homer will always look like Homer and can appear on any number of products or doing endorsements for products and always carry the same panache. Same thing for comics. At some point, the characters and their story become secondary to the marketing. Wonder Woman, the comic, has been a perpetual money loser as a comic for the past half-century, but Wonder Woman, the marketing icon, has been a money maker for Warner Brothers, the parent company of DC, for that same period of time. In order to maintain the trademark, DC must publish the comic or see it revert to the Marston family. So, the comic becomes a loss leader for the lunchboxes, beach towels, and toys that let young girls know that they can also be heroic figures if they wear skin-tight uniforms and have big tits...
But does the story suffer from its longevity? Absolutely. At some point, there is nothing new under the sun, so characters that have been in perpetual motion for 50 years begin retreading the same ground. I finally gave up on superhero comics in the early 90s when I realized that a story I was reading was identical to an Avengers story that I had read in the late 70s. I didn't need to read it again in a different context. I still had the original from the 70s. At that point, I also realized that I had put aside several titles from my large weekly purchase to read later and now had several months of various books that I really wasn't compelled to read because they were the same stuff that the respective characters had been doing for 10, 20, 40, 60 years. In fact, writing my own work for the comic studio at the time was far more interesting because I was hoping to do series that had a predetermined finish. I imagine that this disaffection happens to many readers in the same way that a lot of TV viewers get tired of seeing the same canned procedure (intrigue at the first commercial break, crisis at second, deepening crisis at third, possible solution at fourth, and resolution, fini; the hour is over) every week and have begun to drift to choices like Mad Men and Breaking Bad, which are almost expressly designed to be watched from the beginning, which entails either being there at the start or taking advantage of services like Netflix.
So, does a trio of films in less than a decade necessitate a reboot? Is the viability of the character requiring that or the fact that the story will never end and, thus, must be re-energized every so often to keep it fresh for modern viewers? Is it a question of medium? Or is it all of the above?