Two designers—Charlotte Friis and Maartje Steenkamp—have come up with intriguing products that try to answer that question.
Friis has created her Children's Paper Chair as both seat and entertainment. As the toddler grows into childhood, the paper level decreases, and as a result, your child is always sitting at the right height.
All in all, nice to see designers thinking outside the box.
(If you do have a hankering for the high chair, it was produced for Droog Design and it's available here.)