I am not in favour of a too analytical approach to music, since it should be a way of expression rather than mathematical patterns.

However, I have always found it very useful to analyze compositions while studying them. It looks boring and too big an effort but there's not so much that needs to be done and the effect is worth it.

We can start with the clearest of all classical music, which are the works of the composers of the classicar era. In, say, Mozart's compositions, basic harmonic structures are very visible and their purity and clearness is what makes the music as beatiful as it is. Therefore they are good material for investigating this way of studying.

Without depriving them of their beauty, Mozart's compositions can be seen as only a chain of chords and scales. If you think you have wasted a too long time of your life practising scales, this is one of the moments, when you'll find that playing a G major scale is much easier than remembering and inventing fingerings of G-A-B-C etc.

Of course, music can't be performed like this and it takes still more than this to perform a piece well but awareness of harmonic structures is something that has always helped me learning new tunes. And it doesn't matter if it was Haydn or a jazz standard. Furthemore, harmony has often a strong connection to phrases. It is not the only important thing about performing, but it can help.