Most modern telescopes do have very small f-ratios. i.e. The focal length is not a large multiple of the mirror diameter.
The main advantage of this is that you don't have to build a massive dome to house your telescope in and you also get a larger field of view.
For example, the VLT telescopes at Paranal have a diameter of 8.2-m and a focal length of just 14.4 m. The mirrors are about 20cm thick and weigh nearly 20 tonnes.
The reason that this was not done in the past is I think that a highly curved miror has to be thicker and so it becomes difficult to make such a thing without it deforming under its own weight as you move the telescope about. Some of these problems have been partially solved using various material technologies as well as active mirror supports.
However, these problems still remain and the next generation of large telescopes will use segmented mirrors, which gets around the size/weight problem whilst still allowing high degree of curvature to the overall mirror and hence minimises the size of the telescope and the building it is housed in. Of ourse you then have the technological problem of keeping all the different parts aligned to a fraction of the wavelength of light.
For smaller telescopes, there are now an increasing number of low f-ratio designs which offer portability and a wider field of view. The disadvantages are that you need a bigger CCD and/or smaller pixels to tile the field of view and it it is more difficult to make highly curved mirrors that are free of problems like coma and astigmatism away from the centre of the field.