Your setup makes complete sense, and you are not a dumb guy at all. What you are describing is exactly what Kuboo did: browse the server and stream, without copying anything onto the device first. The good news is that Ubooquity, COPS and Calibre all speak OPDS (its basically a standard format for reading content), so the only missing piece is a client app that streams properly and actually looks nice.
I was in the same boat. I ran Ubooquity and read on my phone with Kuboo for years, then Kuboo died and nothing replaced it. So I built my own reader, OPDSy, an OPDS comic and ebook reader. (Full disclosure: I am the developer. It is a paid app, a one time £3.49, with no ads and no subscription). Ive improved on the design for Kudoo tho (which frustratingly split comics and books into two sepparate folders). Ive also added reading status and memory which was also missing
How it fits what you asked for:
• Streaming, not downloading. Comics stream a page at a time over OPDS PSE, and ebooks open straight from the server. Saving something for offline is there if you ever want it on that cheap tablet, but it is always optional, never required. I basically download some content on my one for when im in a underground train ... but for the most part i stream.
• One tidy bookshelf. You add each server as a source and OPDSy shows them together in one clean library, with a colour badge per source so you can see at a glance where each item lives. Nice to show off to the house visitors. It looks beautiful when you got a bit collection.
• Comics in one place, your other books in another. Because each Ubooquity or Calibre folder comes through as its own source, you can keep your comics and your other books apart and still browse them from the same app. No need to copy books into Ubooquity or duplicate anything.
• Works with what you already have. Ubooquity, COPS and Calibre all expose OPDS, so you just point OPDSy at each one and you are reading in seconds. Each source loads on its own, so one slow or offline server never breaks the rest of your library.
One Ubooquity note, since many apps trip over this: Ubooquity advertises its comic page link as an image, but that address actually serves the HTML web reader, so a lot of clients show blank comic pages. OPDSy detects this and requests the real page endpoint, so comics stream correctly.
It also offers paged or continuous scrolling, left to right or right to left for manga, and it can read your ebooks aloud with your device voices if you ever fancy listening.
You can
download it here on the google play store
Give it a try against your COPS and Ubooquity servers and let me know how it goes. If anything misbehaves on your setup, tell me and I will happily fix it.