I've been doing this my whole life (about 20 years now) with contacts. I started in high school for fun after noticing that my contacts made it harder to see super-fine details at very short distances. I read an article about how some motivated people wore custom glasses which inverted the world upside-down, but their brains eventually compensated and flipped the image they perceived. I started wearing just one contact (alternating right, both, or left eye) and despite a diopter of -3.5 my brain learned to use the blurry color of my uncorrected eye to provide an acceptable level of depth perception while only giving me the sight picture from the corrected eye.
Thanks to an ophthalmologist with flexible practices, I'd later also managed to get some variety in my contacts - a bit higher power for sailing, where extreme long distance sight is helpful.
For activities which require precise stereo vision and/or maximum fine detail (soldering, foosball, skiing, sailing, etc) I prefer two contacts (or none, in the case of soldering). For general daily life I still enjoy one contact - my brain will use the picture from the uncorrected eye for close-up stuff, including computing, and the corrected picture for farther things, like driving. It's not perfect; I have to turn my head a lot more in one direction to check for traffic/etc and sometimes objects in the foreground create a large block of blurry vision.
But it's quite nice for daily life where I constantly switch from activities which are close (computers/reading) to far (everything else).
Like 'heikkilevanto, I may have to go back to stereo vision soon - my eyes are reaching the age where they're not as quick to focus and I don't see as much detail. Close-up work is getting much more difficult with just one eye. I can no longer solder at all with mono-vision, depth perception now only works for longer distances and not shorter ones. And far-vision is losing detail, so having two contacts makes it much easier to ascertain what I'm seeing faster because the detail from one eye fills in blurry spots of the other.
Some people have said that correcting vision prevents the eye from adapting and fixing itself to see better again. I haven't found this to be true. Contacts stay in my right eye better and tend to fall out of my left eye more frequently, so for the past decade I've almost always corrected in that eye and uncorrected in my left. My prescription for both eyes has not changed at all in the past decade - for me there seems to be no long-term change, good or bad, caused by correcting my vision.
I also wear contacts that you can keep in 24 hrs/day for 2-4 weeks, and have not seen any damage over the past 15 years of sleeping in my contacts for up to a month straight. I have annual "digital retinal exams" going back 15 years which can see the types of damage that are caused by sleeping in contacts too much (capillary growth due to lower oxygen, calcium deposits, etc) and there doesn't seem to be anything to note, as well as no significant difference between my right and left eye.