The reason that the giant sequoias are left in the United States is due to a couple reasons, and luck can probably be counted among them. A great number of impressive trees were cut down throughout US history, and numerous giant sequoias, white pines, coastal redwoods, western red cedars, and others were greatly reduced in numbers. You could write a book on some of the giants out there that are now lost to time, but let's focus on the giant sequoia, like the General Sherman tree.

As you likely know, logging was a very important industry in the US as far back as colonial times. With western expansion and ever increasing population booms in the eastern part of the country, logging companies had to move west to find good stands of timber. It took some time for logging companies to work far enough west to encounter sequoias, with the first documented sightings not occurring until the middle of the 1800s, and logging starting not too much later after that. This was also around the time that ideas by men like John Muir and Gifford Pinchot came to take root, ideas such as placing limits on logging and creating a National Forest system to preserve the woods for the future. Places like Sequoia National Park were established in the later years of the 1800s and early 1900s, and are a major factor why we still have these trees around today.

Before the protections we have today were set in place, thousands of the giant sequoias were still cut down. The size of the trees was a factor in their survival, as the average man or even saw team would be unable to easily cut one down. Logging sequoias required very large saws and other investments in time and equipment over more preferable and available species. In addition to the challenges of size, the wood from sequoias is very brittle. Many of the trees cut would shatter upon hitting the ground, ruining them for cutting into dimensional lumber. This made it hard to turn a profit on sequoia logging, especially when large numbers of more usable species were nearby.

With these factors combined, logging of the sequoia stands was largely ended by the 1920s. There would likely be many more trees rivaling General Sherman and Hyperion today had we not cut so many down. Ultimately, the short time period in which the sequoias were logged and the foresight of men like John Muir, Gifford Pinchot, Teddy Roosevelt, and the organizations they founded like the Sierra Club and the US Forest Service and National Park Service are the reasons we can still enjoy these trees today.

As a side note, foresters don't need to cut a tree down to gauge its age. They can use a tool called an increment borer to take a tissue sample of the tree, while causing an insignificant amount of damage to the tree itself.

Sources: Forest Service Database entry on Sequoiadendron giganteum

National Park Service article on giant sequoia history

History of the Giant Sequoia from monumentaltrees.com

Haglof forestry tools page on increment borers

I had some books better detailing sequoia and logging history in the United States, but I may have loaned them out. I will update this post if I find them.