This is where many music colleges and schools lose their student interest and because of this they later can view the chordal analysis as useless. By simply analyzing the chords and never actually doing anything with them is a waste of time and energy from the student's point of view. I propose that we go beyond analyzing chords.
Some of the most important steps you can take here are memorization and transposition of these chords. I'm not talking about the memorization of the entire piece, just the chordal progressions - harmonic outline or a skeleton.
What happens when you memorize a chordal progression of some 8-10 chords? You are beginning the internalization process of the musical language of this piece (and of this composer).
Just like learning any foreign language, first you have to translate the words into your own language so that you understand them (in music - that's a chordal analysis). By learning the names of the chords, their inversions, modulations and cadences, you will truly understand the musical meaning of the piece you are playing.
After translating the words, you have to memorize them so that you remember them later and prepare to use them. In musical realm you can also memorize chordal progressions so that you can recollect them. It's important that you only memorize the chords and not the entire piece with all the notes (unless you want to but this is not the purpose of this post). Entire piece is just an elaboration of the basic harmonic outline.
But internalization doesn't stop with memorization. When you are learning a foreign language, you have to apply the words and expressions to various situations. In music, this is best achieved by transposition. Here you have to transpose the chordal progressions from memory into as many keys as you can. Sometimes even changing the mode from major to minor and vice versa (whenever possible).
By memorizing and transposing enough chordal progressions you will internalize the harmonic language of your favorite composer and you will be just one step away to actually using this harmonic language in your own improvisations and/or compositions.
When I was introduced to this concept by Pamela Ruiter-Feenstra back in 2000, it was an eye opener for me. I hope you are equally excited as I was back then.