I guess they just got tired of the C.W. style Kepi and wanted something more 'modern'.

It appears mainly in National Guard and 'garrison' photos of regular troops.  I haven't noticed it much in active service, during war time, photos.

(But, it is contemporary with the U.S. Krag and I got a repro from S&S Firearms for display purposes).

By 1902, a new 'Bell-Crown' (flared) cap came into fashion and looked more 'rakish'.

Maybe, if the model 1895 Kepi had incorporated ear-flaps, it would have won more hearts!