With a lead sheet, a lot of times the pianist/keyboardist is not carrying the melody. It may be the singer or saxophonist for example. Many times also, the pianist/keyboardist is not responsible for the bass either! The lead sheet format is perfect here. The pianist can play the chord with the left, not necessarily with the root in the bass. The right hand can be left free to wander in and out of the melody, or to solo as desired.
Otherwise, the lead sheet is way more efficient and way easier to read than standard sheet music. When I see the chord name above, my mind is at ease. My hand (left or right) automatically knows what to do, with practice of course. I don’t have to look at the individual notes to figure out the voicing. If I don’t have to carry the melody (or if I can’t sight read it), I usually like to play the root in the left and the chord with my right. I’ll be conscious of the relevant key so that I can sneak in random notes.
Experiment a bit. Enjoy the freedom. For example, when you see “C” in a lead sheet, you can play around with substituting a Cmaj7, Cmaj9 or Cmaj13 instead. When you see “C7”, you can play around substituting C9, C13, Gb7, Gb9 or Gb13 instead. Try it out! You'll see. Generally, a lead sheet is far more forgiving than a classical score.