British Petroleum would lose the well permanently and have to drill a new one.
I love how trolls can get modded +5 Insightful here. Please elaborate on your experience in the oil & gas industry.
I am a product engineer that designs subsea equipment. The company I work for sells equipment to the majors, one of them being BP. I can't tell you the amount of hours people have worked to try and fix this problem. In addition to the people involved, people that have had zero to do with the original Horizon products/well are creating Plan A - D solutions in 24-hour shifts. This is all in an effort to stop the leak as fast as possible, regardless of who has the liability (that will be worked out later).
If nuking it was a viable option, then I'm sure BP would risk losing a well at the cost of re-drilling a new one. The PR nightmare alone is worth that cost. I know it's easy to say BP is evil, but now all eyes are on them to fix the issue. If they create another problem (such as nuking the well), I doubt you would be the first one to defend their actions.
Things are not so black and white. Consider that you're operating in under high pressure (15-20ksi), with minimal access and visibility. Any equipment you send down there NOW has to be taken off the shelf. new designs have 4+ week deliveries (normally 8+). There is no such thing as "plug and play". Each customer, each project is different. So now you are patching together equipment from other clients (off their shelves) to make something work.
I can't speak for BP, but I can tell you I take pride in my work, and my coworkers are the same. We don't release anything that is unsafe. Period. I don't know about this project, but anyone in the industry can tell you that the environmental regulations we design to for Mobile Bay are stringent. No one wants to have this type of disaster.
At the same time, how many PHB's have you had that focused on schedules/costs instead of features/the product? That's their job. People make tradeoffs. I have to say that no PHB I know would knowingly risk damage to people/the environment over making more money. But it's never that clear is it? How do you balance risk and safety? What is the definition of effective? You never have all the metrics to make the right call. There are a lot of people/processes that make this well happen, a problem in any area can lead to this.
Oh, and in case you think I'm a shill, I would love it if we all drove electric cars. But until everyone decides to drop plastics for the corn variety, or gas for electric, you need fossil fuels.