What's wrong with if you only sharpen, and never hone, your knives?

A kitchen knife has two different structures of steel in it; hard steel in the edge so that it can be sharp, and soft steel in the spine so that it can be flexible and tough. The real danger of too much abrasive sharpening is removing all of the hard steel from the edge of the knife, at which point it will become impossible to give it a good edge.

Where I've seen this happen in practice is cheap stamped steel knives (many of which have a fairly thin layer of hard steel to begin with) sharpened using an electric sharpener for years. My mother has some that are basically butter knives now. Forged knives tend to have more hard steel, so it takes a lot more over-sharpening to remove it (still, my mother-in-law has managed, after grinding off 4mm of the edge over 30 years).