You are not required to purchase any lenses at all. It all depends on your photography needs and what you're willing to spend your money on.
Regarding range, the superzoom 18-200 mm covers the same range as the other four lenses you mentioned. All of the other lenses focal ranges are parts of the large range of the 18-200 mm lens. The 18-200 can surely acquire focus at all focal lengths in it's range (as far as I know there are no zooms that can't lock focus in certain parts of it's range).
There are other factors and characteristics of a lens that matters to some photographers, otherwise lenses such as primes that can be a lot more expensive than the not so expensive 18-200 mm wouldn't exist. Some of these factors are hard or even impossible to achieve in a superzoom and if it could be done, the lens would be prohibitively expensive.
Some characteristics that are important in lenses other than the focal length range are:
- Image quality - there are many aspects regarding quality that can make a huge difference to the final result. In some of these aspects superzooms are definitely lacking compared to more moderately ranged zooms and especially prime lenses.
- Maximum aperture, this is important to control depth of field and a large maximum aperture lets you to create bokeh and let more light in. In a zoom lens a constant maximum aperture is helpful since you don't have to change the exposure settings all the time in manual mode when zooming.
- Minimum focusing distance - lenses with a short minimum focusing distance are usually more expensive, but depending how short that distance is it potentially lets you take macro photographs.
- Build quality - there can be a huge difference in quality and feel between cheap lenses and more expensive ones. Zoom and focus rings are usually a lot smoother, the plastics are of higher quality and there are extra features added such as focus range indicators and range limiters on the expensive lenses. Some lenses don't change length when zooming, a feature usually preferred. Also a front element that doesn't turn when focusing and zooming can be helpful, especially when using gradual filters.
- Focusing speed - a fast focusing speed can let you catch moments that you otherwise couldn't (or at least not as easily). However the focusing speed doesn't entirely depend on the lens and the camera body plays a part in it too.
- Focusing technology - There are different motors that are used to move the focusing elements of the lens and some of them are louder than others. Among the more expensive ones are stepper motors and ultrasonic motors which both have there benefits compared to the cheaper ones (and each other). Some lenses change length when focusing and others, internal focusing lenses, does not.
- Image stabilization - this feature lets you take sharp photos at lower shutter speeds.
- Weight and size - lenses with large focal length ranges as well as large apertures can get heavy, the 70-200 mm f/2.8 are great examples of this, usually with a weight of around 1.5 kg. Some lenses are built in very compact sizes, pancake lenses being a great example of this.
- Sensor coverage - some cheaper superzoom lenses such as the 18-200 mm are designed to be used on crop sensor cameras. There are many different sizes of consumer DSLR sensors and they are usually represented as the crop factor that you need to apply when cropping a full frame sensor (the name of the standard 35 mm frame of a film camera). A lens that is designed to only shed light over a cropped sensor can't be used on a full frame (it won't cover the entire sensor). There are also a lot larger formats than the full frame, such as medium or large format cameras and their lenses has to be able to shed light over the entire frame.
Also different lenses have different warranties and quality controls and even if this doesn't necessarily improve the lens as such it can be important to the photographer.
Together they can explain why some lenses are 10 times more expensive than others with seemingly close specifications. Since there are so many different aspects of a lens, every single one that you can buy in the stores are a result of the art of balance between different factors, with price usually being a highly limiting one.
This doesn't mean that you have to buy the other lenses. In fact I recommend that you don't until you know what your needs are and especially that your current gear is insufficient.