The problem here isn't that you can't make a case drilling elsewhere. And you can make a legitimate argument that some locations should be prioritized over others, for various reasons that could very well include tourism. As you go about deciding where to approve leases, things like that are perfectly fair considerations.
But it's a long way from that to what just happened: Last week, the Trump Administration announced that it will lift the ban on offshore drilling in virtually all U.S. waters. Then Florida politicians from both parties freaked. Less than a week later, the Trump EPA says there will be no drilling off the shore of Florida.