This was an interesting summary of the history of Belle Isle. Based on Olmsted's description of what he first saw on the island, we may not want to go completely natural:

Conditions could not be more favorable to the breeding and nursing of mosquitoes…the pools, in September, I found discolored, and covered by bubbles and a green scum; and there was putrescent organic matter on their borders. They are thus available to the propagation of typhoid, malarial, and other zymotic poisons; and it may be questioned whether the city is justified in allowing, not to say inviting, ignorant people and children to stray near them.