Classic archaeology is all about layers. When excavating, a lot of effort is made to determine where one layer starts and where a layer ends. You can often tell eg. by soil color or other hints.

So yes, dredging up the ground destroys all context, and you get finds that are very hard to date (carbon dating and other scientific methods have limited precision if you don't have any reference points)

On the other hand, I guess you take what you can get, and archaeologists often work with finds like that. A farmer might accidentally have dug up some roman coins on their field, or people with metal detectors may find some clothing pins (not sure of the correct english word) or something. These people may also not be eager to tell you where they found it (farmers really don't want excavations on their fields)