As much as I can understand the impulse to stick it to the oil companies, a windfall profits tax would be a terrible idea. In an economy like ours, which relies on innovation by private companies to grow, confiscating profits when we decide someone has made “too much” money makes no sense. We have a tax rate on companies that is set in advance. It would destroy companies incentives to suddenly decide “we’re taking more of your money.”
However, given that the oil companies are busy raking in record amounts of money, it does seem like an opportune moment to take back some (or preferably all) of the $20-50 billion in direct subsidies we give them annually. That would probably bring in more money than any of the “windfall profits taxes” that are being proposed would bring it, plus it would have the benefits of moving the government out of the “we’ll help this company/sector succeed’ business and eliminating the distortions in the market caused by subsidies. And if we really wanted to stick it to the oil companies, we could go after the royalties they owe us for drilling on public lands.