I guess that depends on how you define enrichment. I am also the mom of a "gifted" child - 3, in fact, with one close to the 99th percentile. I also homeschool so I have btdt.
Teaching gifted kids is not just about letting them learn at a quicker pace. It's about satisfying their thirst for knowledge. While mildly gifted children (75th-95th percentile) might be satisfied with a quicker paced regular ed curriculum, most moderate and up gifted children NEED enrichment to satisfy their curiosity.
When we first started homeschooling, I let my kids go at their own pace but when my oldest two ended up 4+ years ahead of their peers after 2 yrs of schooling, I realized it is far better to add enrichment to slow down their academic pace. They were so much happier because they finally were getting what they wanted - deeper understanding of what they were studying instead of the superficial learning they were doing. By enrichment, I mean to delve deeper into topics - much deeper than they would ever get in regular ed lessons; Allowing them to research their interests through projects; doing electives (music, sign language, robotics, computers). They are still a year or two above grade level, depending on the subject but they have a much deeper body of knowledge, which should serve them better in high school and college than if they just blasted through the regular ed curriculum, graduating years ahead of their peers. Of course, I suppose I could had also gone the route of just sticking with the regular ed curriculum and schooled only about a 1/3 of the school year....
So the value of enrichment really depends on how you define it. I will agree that the enrichment most schools do for their gifted students really is just extra busy work. It would be better if they would modify their regular assignments to provide true differentiation so that the students are not being punished with more work just because they are quicker to grasp concepts. But this rarely happens.