There are three methods of character progression. One is doing the level up, the second is learning as you go, and the third is a hybrid of the two. Now in games that uses the level up system showing the statistics is vital because it gives the player a concrete understanding what his or her character can and cannot do. Its a method used in many CRPGs and it is the closest method to PnP RPGing
Having you character learn skills and abilities based on what the character does has its own strengths. It actually forces the player to make use of the skills he or she wants to focus on instead of letting the player choose to level up and spend his points on abilities he never worked towards. It actually pushes actual role playing but at the same time the game does not necessarily needs to show character statistics and other metagaming material for the player to gauge the strengths and weaknesses of the character. I have yet played a game that uses this method satisfactory in a Single Player CRPG.
Then there is the hybrid which uses a combination of both systems to some degree or another. A good representation of that is Morrowind.
Personally I like the level up system, but if we can geta good story driven game that uses the second method to its fullest potential I think it could be fun.