Fed lands, state lands
Utah's federal lands contain priceless natural beauty and spectacular archaeological treasures. Under state control, preservation of these lands and public access are very much at risk. Assurances from the governor about the state and federal interests being complementary aren't going to change a bad idea.
But if you are curious about how Utah might protect recreational land and don't have a problem with user fees/taxes, I have a perspective from hiking a number of trails at Wasatch Mountain State Park. With one exception, none of the park's trails meets commonly accepted standards that are almost universally found in a National Forest.
If these standards were followed, equestrian riders, mountain bikers and hikers would more safely be able to accommodate one another. One reason for substandard trails is that there is no funding; volunteers do this hard work.
Even if the feds wanted to give us these lands, I do not believe Utah is capable of managing its current state land commitments, much less a greatly expanded portfolio. Extracting every drop of oil and gas will not significantly reduce our dependency on either commodity.