That's what Dolby would like to believe you. The quality of projection in theaters is actually pretty bad, the same can be said for audio. I agree with what you say. The installation in theaters are nowhere near 5000:1.The king of theater (projection) video quality in the U.S. are Dolby Cinema theaters.
The point is, you can do a lot better at home with a proper setup. Certainly not with a $1500 projector though. What you describe is what you get with a $1500 at home, a dim and flat looking image, but in the theater case with a more expensive projector on a much, much bigger screen. That's why the whole package is important and not just a single component. I've already mentioned a few things about black levels and so on. To a certain degree this is a non-issue with intrascene contrast. It's visible when you look at a black screen. If you want the highest on/off CR with the lowest black level and still a good, despite not DLP-like ANSI CR, then your best bet is Sony. But again, it depends on your screen size. You can always double stack, which some people do. Sony claims a quad stack is an option, but I've never seen it in the wild, only in Sony demos. Pick something with the highest ANSI CR, but still good enough black levels and on/off CR. The whole 300k:1 stuff is marketing nonsense.
In addition to that, you can do the same with a HTPC as a source. And there's the upcoming madVR box. Don't get me wrong, Jim knows what he's doing with his processors. I've been Beta testing their stuff for ages, before they were actually released to the public (I think I still have one of their HDPs in the basement, which I ran with a Barco 9" CRT projector). But it's time for some competition.If you want the best possible picture you purchase a Lumagen video processor which actually produces an HDR image in an SDR container.
Calibration is something most people forget. They just buy, set it up and are done when a proper calibration can make a night and day difference. Also, unless prices have changed, the $10k is for the biggest 4446, the others are cheaper.Obviously you need a good calibrator to make all this happen. I did this with my Sony 4k projector/130" screen and at 12' the picture is stunning, absolutely stunning. The video processor (Radiance Pro) will run you about $10k and $1k for a decent calibration.
It's also well worth it to consider the use of an anamorphic lens. Which means you won't have a brightness drop when watching scope movies. Another option when projection + processor + lens is considered would be something like a cinemascope Barco projector, which comes with a scope format DMD and does everything a processor does in it's firmware. So no Lumages required in such a case. The other solution would be more modular though, so processor + lens can be kept and the projector swapped out for a new one. This is all a moot point when $1400 is the budget. A TV is the much better option in this price range it just comes with a really small display in comparison.