Well, first, Larson was no more "of the street" than Sondheim. As someone who lived in the East Vilage during the early and mid-90's and lived part of the life depicted in the show -- half my friends, straight and gay, were living with AIDS and I was friends with a lot of the squatters on 13th Street -- I saw "Rent" with several friends from the neighborhood when it debuted at New York Theatre Workshop and none of us were impressed (several walked out at intermission -- I stayed only because I thought there was a song or two that worked).
"Rent" had/has nothing whatsoever to do with the reality of living in the East Village in the 90's. The rumor around at the time was that it must have been written by somebody from Westchester or someplace similar who had maybe visited the neighborhood once or twice in the past, because anyone who actually lived there couldn't possibly have gotten so completely wrong. The music and the sensibility of the show felt entirely suburban to us -- the music was entirely disposable 70's middle-of-the-road pop and light rock -- some decent lyrics, but the SOUND was laughably, exactly the kind of stuff our out-of-town relatives thought might be cool.
In contrast, when "Hedwig" debuted a couple of years later, everybody I knew from the neighborhood freaked out and embraced it -- the score captured exactly what was happening musically at the time, to the point where, for a time, nearly every bar in the East Village had the cast album on their jukebox (a first, I believe, since the East Village has never been big on musical cast albums -- "Rent" NEVER made a single jukebox in the neighborhood, though I recall that it got played and booed by the crowd once or twice as a joke).
Larson was certainly quite promising (and he and Sondheim were friends at the time -- Sondheim believed he might be an important composer, being able to bring contemporary musical influences into the musical theatre). Larson never got the chance to fulfill his promise and even he knew that "Rent" wasn't a finished product during that last workshop at NYTW. While Larson was certainly talented, he hadn't quite figured out how to take truly contemporary rock and R&B music (i.e. from the 90's, not the 70's) and use it within a musical theatre context ("Hedwig" was a far closer reflection of that -- heck, even "Dreamgirls" sounded closer to the music actually coming out of most people's radios than anything in "Rent"..... the reason the "Rent" is still running is that "younger" traditional musical theatre fans in their 40's and 50's find the music to be close to the kind of pop music they grew up on).
So anyway, the original question was (I think) could Sondheim have written "Rent?" I doubt he'd have wanted to, being a child of the 40' and 50's, classically-trained and very much in love with the possibilities of an orchestra, more so than with what one can do with a small rock combo or a synthesizer. However, one looks at something like Sondheim's "Unworthy of Your Love" from "Assassins" for example -- a very catchy 70's style guitar ballad that Glenn Campbell or James Taylor would have been proud to have written. It's not the sort of thing that Sondheim is known for, but more so than perhaps any composer, he's able to adapt his style to suit and speak for a given character (whether the character "sings" in 19th century British musical hall style or 20's vaudeville-style or Japanese-inflected art song or 60's "mod" style). Hinkley, being very much a child of the 70's, Sondheim found the ability to write a song in the voice of the singer-songwriter style of that time.
Could he write an entire 70's-style score? or 80's? or 90's? He's and old man now, so I sincerely doubt such stuff appeals to him. But COULD he? I wouldn't put it past him.
"What a story........ everything but the bloodhounds snappin' at her rear end." -- Birdie
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"The Devil Be Hittin' Me" -- Whitney