Sadly it's not everyday that I get the time to work out tunes that I'm practicing in different keys - let alone all of them.
Having said that, I see that the benefit of working on a tune in at least a couple of other keys is enormous.
The first thing for me is that if you practice say 'Autumn Leaves' in A, as well as G then you are simply going to play it differently in the new key. You will play licks and patterns in A you won't naturally play in G. If you then take the time to observe these ideas and then work them back in the original key, it gives you a huge amount of new material.
Add to that a few more 'difficult' keys, then you really have a good thing. Practicing phrases in the keys you can naturally play them is one thing but in the harder tonality, you probably don't play them as well. Any practice here will help a lot.
With the piano, when you comp the same standard in different keys, it adds a wealth of depth to the colours you can use. Sometimes you use a different voicing in a higher or lower key that you wouldn't of thought of in the original key - but still sounds nice if it's used.
One can also try using the transpose function on the piano/keyboard. Comp the tune sounding in the same pitch, but play it in a different key. This allows your ear to discover new voicings that you might like to incorporate in the original key.
This I do quite often. Back to Autumn leaves, I'll transpose the piano down two semi tones and then comp the tune up two semi tones. I.e you play in A but the piano sounds in G - the original key you were working on. It leads to amazing results. As soon as you hit a chord that is different you will hear it. It can really add a new dimension to your comping.