Fast prime lenses like the Canon 50mm f/1.4 lens work nicely in low-light situations. But I'm quite sure they would work even more nicely if they had optical image stabilizers. It seems to me that no such lenses are available in the Canon system. Is this true? Maybe even for prime lenses in general? If yes, is there a reason for this?
As of today there are 38 prime lenses with image stabilization. Almost half (16) of them are from Canon and 2 are Canon-mount Sigma (data from these search results at NeoCamera).
What you will notice is this is less common in the wide focal-length, with the only wide-angle stabilized lenses being Canon's 24mm, 28mm and 35mm, (all others below 100mm are designed for 1.5x or 2x crop sensors). This is because longer lenses benefit more from stabilization because they require higher shutter-speeds to give a sharp image.
Take for example a 500mm which would require 1/500s. This stabilization you can take it down to 1/125 or 1/60 even which is still a general purpose shutter-speed. Now take a 50mm which already gives a sharp image at 1/50s, you can bring that down with stabilization to 1/15 or 1/8 even. Those shutter-speeds are not suitable for moving subjects and even grass and leaves will blur. Now, of course, all shutter-speeds are useful, just that you gain more by stabilizing a long lens than a short lens. As a matter of fact, some people ask why certain wide zooms are stabilized, saying it's a waste of money!
Prime lenses with image stabilization do exist, and I believe they will become more popular with time.
One great example of the implementation is the Canon EF 100mm f/2.8L IS USM. It provides 4 stop hybrid image stabilization, great for angular as well as shift movement. A 50mm prime will not benefit nearly as much as a 50mm, especially when you start considering macro capabilities.
As you go up the range, you will see that many prime lenses offer image stabilization, just in the situations that benefit the most from it, long telephoto prime lenses. Examples: 200mm f/2, 300mm f/2.8, 400 f/2.8, etc.
I think the main thing that it sounds like you are looking for is a wide angle or normal lens with image stabilization. For prime lenses that are wide especially this is not as important, but I do not believe any technical reason exists why this is not implemented. It more likely is just not sought after by most for price, weight, and size considerations.
The Tamron SP 45mm F/1.8 Di VC USD is the exception to the rule: https://www.tamron.eu/lenses/sp-45mm-f18-di-vc-usd/
I own it and use it on the EOS 6D, it is a very fine lens with image stabilization and weather proofing too.
The Canon EF 100mm f/2.8L IS USM is the first thing I thought of when I read this post...
But it is true that you don't tend to find them at the wider end; simply because you can get away with slower shutter speeds and so the fast aperture is in itself enough to get you the sharp shots, and the addition of IS would add weight, cost, and something else to possibly go wrong! :-)
Do keep in mind that there would still be a big factor limiting the use of eg an f1.2 stabilized prime: If you are in the shutter speed range where camera shake becomes a potential problem... subject motion also does. People, foliage, vehicles... move. Neither OSS nor tripods help with it. One reason to use ultrafast primes wide open in low light situations - despite their disadvantages (heavy, flare prone, in many cases spherical abberation and coma ridden, difficult to handle DoF) - is allowing for subject-motion-proof shutter speeds.
Also, the way OSS systems appear to work is very similar to decentering the lens. Ultra fast primes are sensitive to decentering. While the ultra-shallow DoF can help composing around static decentering ... having to deal with dynamic decentering effects could become very frustrating quickly... and god knows what that will do to a lens using large aspheric elements (a purely spherical design that fast will be great to use on people wide open at night, usually NOT on infinity subjects. People=subject motion....).