Inter-classification of organic chemistry functional groups (carboxyl vs alcohol & ether vs ester)
Would it make sense to classify a pistol as a type of pipe? The barrel of a pistol is a cylindrical metal tube, after all.

Clearly, no. The other key defining components of a pistol (stock, trigger, etc.) combine with the cylindrical metal tube to radically change its function and behavior.

Similarly, even though a carboxyl group does contain an $\ce{-OH}$ group bonded to a carbon atom, its behavior is sufficiently different from that of an alcohol that it makes no sense to group them together. A parallel argument holds for ethers and esters as well, as ably noted by MaxW.