I have read lots of articles that argue that the less you carry with you on trips or in everyday life, the faster you will be taking photos and you will take full advantage of your gear. However, how can one lens cover all the situations you might encounter? If I carry a 50mm 1.8 lens, for example, and my object needs a telephoto lens, then I'm stuck. How can I travel light and still be able to handle whatever situation I encounter? How do you handle similar situations?
There is a trade off between image quality and size. The smaller your sensor, the easier it is to cover a wide range of zoom distances and the lighter and smaller your lenses can be, however, they also collect less light and produce lower quality images.
You have two main options for keeping things portable. You can either specialize in a particular type of photography and limit your flexibility. This allows you to use a higher end camera and lens without getting to heavy or bulky, but you can only handle the situations the gear you have with you can handle.
The other option is to give up quality in exchange for adaptability. Mirrorless system cameras and even point and shoot cameras are very light and use smaller sensors, which limits the image quality they can achieve, however, it radically simplified and miniaturizes the lenses so that you can handle a much wider range of situations on the go.
No one answer is right for everyone and to decide between them you really have to evaluate which is more important to you. Most things in photography are about judging trade-offs to achieve your goal with the best possible result. Quality doesn't matter if you can't get the shot you want, but if you know what you want and can narrow down the gear, you can get better quality.
There's also the third option for the crazy ones of us out there who decide that they would rather compromise on size and weight and bring their whole setup with them wherever they go and just deal with it. A good selection of cases and learning to predict what gear you will need for a given situation can be helpful if you really want to maintain the best quality regardless of portability.
Sounds obvious but limiting yourself to one lens is going to be limiting, Period. You can get a lens with more coverage in terms of focal-length or aperture-range but there will always be something outside of its range. Have a 28-300mm? What if want to shoot extra-wide, say 14mm? or extra long, say 400mm? Or make a very blurred background? I'm guessing you get the point by now.
The true solution is to change what your needs are. Work with what you got. This is what will drive you to be more creative, not having every tool in your arsenal. The more limited you are, the more creative you will have to get to make a meaningful shot. instead of taking a typical wildlife close-up with a 600mm lens, try it with a 24mm and see how you can get the animal in context with its surroundings, for example.
Another alternative is to do cropping from a wide-angle lens, e.g. mounting a 28 mm lens on the Sony A7R with 36 MP means that you can get the equivalent of a 56 mm focal length at 9 MP resolution, or even "longer" if you are fine to drop further in resolution.
As long as you are pairing a high-quality lens with a high-resolution sensor to adequately resolve all the details captured, there is only going to be an insignificant drop in perceived image quality.
The idea of being able to cover all of your needs -- regardless of the lens you have on your camera or the lenses in your bag -- is a fallacy. No matter how big your kit is, you are going to come up against situations where you don't have a solution.
Outside, you see that bird you want to get a photo. Maybe you've got 200mm of reach, or even 300mm or 400mm. But you know what? You're going to say "if only I had that 800mm f5.6!"
Inside, you want to take a photo of your family sitting and laughing. You grab your 24mm lens and back up and hit the wall, but some of your family is still cut out of the picture. If only you had the 20mm lens!
It's spring and everything is in bloom and you want to photograph that flower. If only you had a macro lens to better capture the pistil! Or, if only you had an extension tube to get closer!
There is a constant stream of scenarios where the kit you have just isn't adequate for everything you might want to photograph. This is where you need to work to establish your own preferences and vision for your photos. Personally, for every day photos, I use a 35mm f1.4 lens and it lets me capture just about everything I want to capture.
As rene says, the point of one lens (for me at least) is not to shoot everything, but instead learn to see. I have been shooting 50mm lens for 3 years exclusively and now i am in my second year with 35mm. Now i can immediately see what the picture would be like without taking camera out of the bag
Image quality, small size, coverage. You have to pick two out of three I'm afraid. You could get the latter two by having a single superzoom lens, the former two by taking a small number of primes (e.g. the Pentax DA Limiteds, the Olympus 12mm/45mm/75mm), or the first and last by taking a set of 17-55 and 70-200 f2.8 zooms.