I casually collect. I have portraits of anonymous subjects - from garden-variety vernacular daguerreotypes to high-end late 19th-early 20th century studio portraits. I find them fascinating as windows into people who otherwise are lost to time. I also have quite a few cartes-de-visite of known subjects (mostly Mathew Brady cdvs, but a few by others), and a decent collection of circus sideshow performers whose identities are known, some of whom are famous (Tom Thumb and his wife, Madame Sherwood the fat lady, etc). The "celebrity" photos (for lack of a better term) are more a reflection of the culture of the time in which they were taken, as their images would have been sold and shared as a form of cultural currency. And there are a couple of daguerreotypes in my collection that I am proud and humbled to be the custodian of - one is an anonymous daguerreotype, but taken by Mathew Brady, and the other is a daguerreotype of William Maxwell Evarts, as a young man. If you're not familiar with who he was, he was an attorney for the state of New York in the 1850s who co-wrote the winning argument in the case of Lemon V. New York, which was the case that declared an enslaved person brought into a free state was automatically free. He went on to be the Attorney General of the United States for Andrew Johnson, and Secretary of State under Rutherford B. Hayes. I look at both of them and appreciate the aesthetics of the anonymous portrait, and the history represented by the Evarts portrait.
To me, I don't think it matters much who the subject is, or if I know who they are. I buy all kinds - anonymous subjects, subjects whose identity is known but are not famous, and "celebrity" images. They're all fascinating in their own way. I think with "celebrity" images (especially modern ones), for me to collect them it would require them to be a higher aesthetic standard. For example, I wouldn't buy a paparazzi snap of Queen Elizabeth II, but I would have no objection to owning the Annie Liebowitz portrait of her in her regalia standing in a field in Scotland (not that I could afford that image).
Street photos are another animal altogether. For them to be interesting, they NEED to tell a story. The identity of the subject is at best secondary, and in most cases either irrelevant or even a distraction. Think of the Diane Arbus photo of the boy with the toy grenade - the story the image tells is far more interesting and important than the back-story of the boy, and if we were to know it, it would become a distraction and diminish the image because we'd be talking about the specifics of the child's life story, rather than reading it as a universal tale. Or at the very least, it would completely change the narrative being told.