I've been testing out digital minimalism and part of me started to think about having a camera without constantly looking at the display. I have known about a bunch of the Leica digital cameras without LCD/Display but unfortunately those cost a fortune. Instant camera are also the next best things but each of those film are really costly.
You mean for a viewfinder, or as a data display? Most regular DSLRs have a display that's switchable between each display type, or you can just turn it around so it faces into the body & close it.
You would still have the basics of your exposure triangle & focus confirmation in the viewfinder itself.
I think you (and others thinking about something like this) should not prematurely dismiss film. I have a Rolleiflex TLR which I love using. People shoot different quantities of images, but to give an idea, since I got it in April 2017, I've shot 33 12-exposure rolls of film. My last 5-pack of Kodak Portra cost £57, and my (good) lab charges £10 for developing and scanning. So my per-exposure cost (after having bought the camera of course) is about £1.80 per exposure. This might sound amazingly expensive, but that also works out at ~£700 for 4.5 years' worth of photography, whereas many digital cameras will cost 2 or 3 times as much. 35mm film would be cheaper I guess, and if you do development/scanning yourself, that could potentially reduce costs too.
Now, of course, people are so used to the "unlimited" photography that digital allows, they might balk at the idea of shooting only 400 exposures over 4.5 years. But for some people, this can be an option to consider. I love the results I get, and I rarely do any post-processing beyond a little basic rotation and cropping.
(Caveat... I don't only use the Rolleiflex, so I'm shooting more than 100 exposures per year in reality. But I just wanted to present this option as something that could suit some people.)
Sony DSC-R1 may be worth a thought. Its 2" LCD folded on top of the camera is nice for framing, but kind of useless for "sneak-peaking" since the optics and resolution of the camera are so much better than what the LCD can show that you don't get to recognize more than complete failures in advance.
Disadvantage, of course, is the bulk of the camera and a light sensitivity to be expected from a CMOS sensor 2005 A.D., even if almost APS-size, accompanied by autofocus (and general camera) speed and precision and media access times also in the contemporary ballpark. Not an action camera, and for indoors there is not a lot of leeway around using flash.
Whether it is enough to help against your chimping addiction is an open question, of course, but it does encourage a "shoot now, view later" mindset at least more than modern cameras would.