Having the zoom can certainly be useful. Technique (such as using a timer mode) and optical image stabilization can help account for many of the problems you described.
That said, there are other costs associated with a super zoom that must be considered. Any lens design involves compromises. For a super zoom, either the cost goes up or the quality of the lens has to go down. It's hard to make a lens that covers a longer focal range, though it is made easier by the very small sensor in a point and shoot. Compared to a point and shoot with a smaller zoom range and a similar value and price however, the shorter zoom would be expected to have a better quality averaged across the focal length range.
Maximum aperture across the focal length range is also something to consider as the maximum aperture typically becomes much smaller (bigger number) as the focal length increase. This means less light can make it to the sensor when you zoom in.
Lastly, there is the consideration of point and shoots in general. With such a small sensor, your ability to get good depth of field, your low light capability and your overall image quality will be greatly compromised when compared to cameras with larger sensors, such as a mirrorless system camera or a DSLR. Additionally, the shutter lag is generally much more significant with a point and shoot which can result in missing a shot entirely.