This is a standard rule in classical 4-part voice leading that applies generally to all voices except the bass, and of course the melody. The bass is normally expected to follow the root movement. In order for the bass to move to the nearest chord tone, it typically must play an inversion. And yes it can sound great, but it's not something you do continuously as it changes the mood and sense of motion created by the harmony in a way that is not necessarily intended by the composer. Also, it doesn't always sound great.
Of course, there are times and places where you can get away with playing inversions in the bass. In the following, a descending line is strongly implied by the harmony, and it can get boring to just sit on the root after you play through the form several times:
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Depending on tempo and style, you might play a linear descending line (D, C#, C, B) over the top four bars...but keep in mind this makes a significant change to the way the chords sound and feel. (D = root, C# = Major 7th, C = minor 7th, B = Maj 6th. This line is really the only thing going on harmonically over those bars. There is a good chance that a guitarist or pianist play will spice it up a bit with different voicings and possibly alterations to the chords, and the notes you play will influence the notes they play.
Here is another tune that implies the same exact descending line:
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Of course, in the C Real Book, "My Funny Valentine is in C minor:
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So, the descending line would be: (C,B,Bb,A)
If the composer actually intends the bass to play inversions, they may use slash chords such A/C#. The top of the slash chord specifies the chord and quality, and the bottom specifies what the bass is expected to play. So A/C# is an A Major with a C# in the bass. So in this way, playing an inversion in the bass can be viewed as playing a different chord. Furthermore, consider D-6 (D,F,A,B) in our examples above played with the B in the bass (B,D,F,A): This spells out B-7b5.
There are lot's of other times in jazz were emphasizing an upper chord tone in the bass really does imply a different chord. Keep in mind jazz harmony tends to be complex and include lots of extensions and alterations, so changing the bass note can easily result in forming a new root position chord. In fact the chord may not even function as written.