Umm - I guess it depends on how natural wonders are being taken care.But yes ,I think we should to protect.
Mount Rushmore was an early form of graffiti, a glorified political billboard. An image of Mount Rushmore, or Six Grandfathers, as the Sioux call it, before the faces of the four “Founding Fathers” were carved into it
As much as reasonably possible, yes. But if there is a conflict between protecting them and human needs, I think human needs comes first.
If a tree fell in the forest and no one was around to hear it, would it make a noise? That said... If it is a natural wonder of the world and no one observed it, would it still be a natural wonder? Of course we should preserve those things not only classified as natural wonders but also as much as the natural substances the earth has to produce but to what extent? Should we deprive all observation by anyone with the exception of a select people or ban observation completely or allow all to enjoy what has been given to us but under certain rules that allow the tracts and objects to be protected? We in the U.S. have many protected parks and travel areas whereby the public is allowed to enjoy what is there but on the other side of the coin we have thousands upon thousands of acres of beautiful land that federal law has mandated that no human foot is allowed to touch. (Except for some privileged few). To paraphrase Epictetus: God has made color but if we could only see black and white, how then is God glorified? Certainly, everything on this earth, especially those things that would give us a sense of awe should be protected but not to the extent that it cannot be observed.
This reminds me; the number of people taking "selfies" and falling into the Grand Canyon is on the rise. Do they not see that really big hole behind them? (Deep thoughts from a shallow mind. )
We should preserve them because we enjoy them. When it comes to the point where preservation means that we can no longer enjoy them, then we're wasting our time and efforts. When we think of the natural world, we are trained to picture the plants, the rivers, lakes, streams, and wildlife, but we are taught to view mankind, and anything connected to mankind, as being apart from nature. Animals act to meet their needs, and most everyone accepts that. A deer will destroy new saplings because it needs to eat, and a lynx will kill a snowshoe hare because that is what it eats, and that is all a part of nature. However, mankind has long acted as if it were outside of nature. Acting in what we believed to be our best interests, we have tried to shape nature so that it would better serve our needs. Afraid of some animals, like wolves and bears, we blamed them even for things they weren't responsible for and began a campaign to eliminate them from nature, and we introduced other creatures, such as earthworms, to places where they were not because we believed they were beneficial. In other words, we acted to meet our own needs, and in obedience to God's instructions to have dominion over the earth. We weren't necessarily always right in the things that we did, but we did them in order to meet our needs. In recent years, we have been encouraged to act against our own interests but that should not be surprising, given that the people who are at the top of that campaign have expressed their desire to eliminate eighty percent of the human population. The surprising thing is the large numbers of people who are leading themselves to the slaughter.
The natural wonders as I think of them are not to useful to mankind except to be seen. The original list of the 7 natural wonders seem to me to be pretty much indestructible. The Grand Canyon Parícutin Northern Lights Victoria Falls Harbor of Rio de Janeiro Great Barrier Reef Mount Everest https://www.worldatlas.com/articles/the-seven-natural-wonders-of-the-world.html Warnings work for those that care about what is to be seen & appreciated, but there are those that don't. Other than trash I'm not sure how humans would change the natural wonders. So any protection from vandals as I think about it would be a yes they are still natural.
I'd need to know how old (and how lasting) the natural wonder is. It also depends on how unique it is. I don't like to see things of long-lasting beauty destroyed for some immediate and transient benefit, no matter who the beneficiaries might be. That being said, all rivers are natural wonders, but that does not mean that no hydro-electric plants should not be installed. Besides, the planet has its own catastrophic events, and nature finds a way. A subordinate question might be "If you agree that they should be protected, do you trust any governmental institution to do anything but use the power to its own benefit and in the process screw the planet more that it would otherwise have been?" Since I would answer "No," I would not even have to consider the question in the first place.