No. Because it is against the law to leave your five year old son at home unattended when you leave the country on a buisness trip even if you're both CIA agents. I take it you've never read the comics.
After Spider-Man 3, I don't want coincidences, and Peter's parents leaving Aunt May and Uncle Ben before they leave(to die) will feel like one.
I'd rather have Peter's parents leaving Peter with a babysitter, and that's when they died, so in other words, I wouldn't really care to see his parents, unless we get some flashbacks, but that's only if the parents knew a villain, possible Osborn, or, and this is a BIG or, if we are introduced to Eddie Brock and we find the parents connection through that way(and I definitely do not want to see Brock nor do I want to see Sony mess up Venom once more. So my next best suggestion is Osborn. Perhaps OsCorp had a contract for the CIA?).
A more street-level-cop feel for this one would be great. Although the cops did do somethings in the Raimi trilogy. Remember Peter was actually following the cops in order to get to his uncle's killer. They also went after the Goblin in SM1 and got clobbered. They told Doc Ock to put his arms up and then they got clobbered. They also went after the Sandman multiple times in 3. Not to mention the tv news broadcast we saw of them going after Venom and Sandman. Most of his villains are way out of the cops league, but I think they could make it street level and still make it work.
I should have given more detail to what I mean. What I meant was, I didn't want random cops to get knocked down and et cetera, I wanted a known cop in the universe to help Spidey out, to get his men and himself right in the middle of a situation with a villain and not back down. Batman had Gordon, but Spider-Man has more allies wearing the blue, and I want to see that. Gordon isn't the only brave cop out there, we've got Stacy, DeWolf, hell, even Stanley Carter can get a swing(before he becomes a madman).
We definitely need a name for a face of a police officer in this reboot, perhaps even two or three. And with a certain cop's death(Stacy), it would definitely be nice to see that add more fuel for Peter being the hero he is. And also give a dynamic for Peter wanting to protect Gwen even more, and if we're lucky, we could see both Stacys dying in this reboot series, which, more than likely won't happen, but it'll be cool just because deaths will only make a hero move further in his bid to rid their city of evil.