It also has some advantages, although some of these have been mostly lost in humans.
In sharks for example teeth get continuously replaced, so losing one is much less of deal for them. This true in reptiles too, e.g. a lowly gecko can have 1,000 new teeth their lifetime. (The more technical term is polyphyodont.)
It is somewhat of a mystery why mammals lost most of this ability, but it is thought to be related to the specialization in the shape of the teeth. Species that have little differentiation between teeth [types] are most prolific at replacing them. (I guess you're ware that humans get two sets, but this is driven by age rather than by a loss process.) There are few polyphyodont mammals as well: elephants, kangaroos, and "sea cows".
Being able to replace teeth in smaller increments (i.e. individual teeth) is probably an advantage as at any given time only a small proportion would be missing... although as with other things in evolution there are some exceptions. Piranhas actually have quadrant-fused teeth (which basically act like larger serrated knives)... and they replace them in whole quadrant increments. (They also grow the replacements in such a way that it takes only about a day for the new set to replace a lost quadrant.) However this is almost certainly energetically expensive, which is probably why few other species have this feature.