Here are some of the strengths of transposition for the prospective improviser:
1. Transposition develops musical thinking. By forcing yourself to play a fragment in unfamiliar keys, you are creating a new musical universe which didn't exist before. Just as we can tell a story in our words, we too can create a musical story out of these musical elements.
2. Transposition improves your memory. In this case, we transpose from memory. Basically, we have to memorize a fragment in an original key and then try to recreate it in another key without looking at the score (except when we transpose by changing clefs and/or key signatures and looking at the score).
3. Transposition helps you to master any key you want. Don't use your key knowledge limitations as an excuse not to transpose. Don't say "I'm not good at playing with many sharps or flats." Simply master your fragment in a key without any accidentals (C major or A minor), then add just one sharp/flat (G major, E minor/F major, D minor). It's that simple.
4. Transposition develops your technique. Have you ever wished that your favorite composers created special exercises for you to practice? There you go - any fragment of any piece by any composer can become a potential exercise which will develop your finger and pedal technique and hand and feet independence. Have created something worth remembering yourself? Transpose that fragment and it will stay with you wherever you go.
5. Transposition helps you to master the styles of your favorite composers. Have you ever wished you could improvise a polyphony like Bach, choral ornamentation like Buxtehude, chromatic chords like Vierne, or colorful modes like Messiaen? Transpose their fragments and they will become your own.
Although transposition is so powerful, it doesn't come with potential pitfalls:
1. Potential to transpose without thinking. This is especially evident in advanced keys. Your fingers guide your mind. Reverse this process by analyzing the chords first and directing your fingers with your mind.
2. Potential to make your improvisations lifeless. There is a tendency to play your fragment exactly as it is when you improvise. Do this frequently and your playing will lack the spark of unexpectedness or freshness. Instead, adapt and transform your fragments so that your listeners would never know where you are leading them.
3. Not all transpositions work in major/minor equally well. Sometimes this is due to the fact that chords that in major mode are minor, in minor mode become major and vice versa. Also some progressions and passages involve progression from 6th to 7th scale degrees. In harmonic minor this interval becomes augmented second which doesn't sound well (because of the 7th raised scale degree). Usually treating a fragment in melodic minor (raised 6th and 7th scale degrees) solves this problem.
Still not convinced? You never know the true power of transposition, unless you try it. Grab a fragment of 1-4 measures, analyze and memorize it, and start transposing. And don't forget to share your experience with all of us.