Why do my Photo Stream photos also show up in my main Photos library on my iMac?

Your screenshot is exactly my iMac settings, and my iPhone has both iCloud and and Photo Stream turned on. What happens after 30 days? Will the photo disappear from both Photo Stream and the main Photos folder on my iMac, but remain in iCloud? Or will it disappear from only Photo Stream, and remain in both Photos and iCloud?

Photos in Photo Stream also automatically appear in the top-level Photos folder. What I don't understand -- does that mean the photo is preserved on my iMac, or is it going to disappear from both Stream and Photos in 30 days?

That's exactly what I'm doing, finding the system that works best for me, but I have to understand how the options work to make that decision. I have often, like you, connected my iphone and dumped photos, but I'm thinking of using this more casual method, which is a good way to characterize it. I'm glad to hear that they stay on the Mac after they disappear in 30 days from Photo Stream, because that makes things very easy. But why does a photo disappear from the Photos folder if I manually delete it from Photo Stream? That's what made me concerned that it would not be automatically preserved when it automatically deletes in 30 days. If you are correct, then the photo apparently does not become permanent/preserved on my Mac until the moment that it automatically deletes from Photo Stream. Before that moment, deleting it from Photo Stream also prevents it from being preserved in the Photos folder. I could not find an Apple Support page that explains this.

Yes, saw that page. It explains, as you highlighted, that deleting from Stream removes the photo from Photo and iCloud. That much I have understood from the beginning. You say it is expected that I will copy the photos from Stream to wherever I wish to keep them. That's how I assumed it would work -- that I would move or copy the photos from Stream to Photos if I want to preserve them in the Photo library on my Mac. But when they go to Stream, they also appear in Photos, so it's not possible to move or copy the photos from Stream to Photos, because they are already in both places. So the question remains: are photos automatically preserved in Photos (and thus, the Photo Library) on the Mac at the moment it disappears from Stream after 30 days? According to m_barrett, that's what apparently happens, but the support page does not make this clear.