Who should decide which method is used in agile organisations?

If your whole organisation works with agile methods and only one team decides something else, then it won't work.

Honestly that same statement applies if you flip it to a team wanting agile methods but the organization does not. And the way you have phrased your post it almost seems like that could be the situation.  In order for anything to be successful in a organization, the entire organization needs to support it in some way.  I have seen success in organizations where each team was given autonomy in the way they choose to work but it required support at all levels of the organization and a wide knowledge of agile practices so that the entire organization could know how what they did impacted/affected what others did. 

An organization can be agile in many ways. A single methodology/practice/framework does not make an organization agile. A common way of working does not make an organization agile.  The ability of an organization to acknowledge change and adapt to those changes quickly and efficiently makes an organization agile.  

So what is your opinion, should the management decide which methods should be applied, the PO or really the whole team?

My opinion is that the entire organization/company has to agree that they want to be agile.  It has to provide the support for teams to be self-managing, self-organizing to the point of being agile.  It has to agree on what success looks like and set some shared goals.  The organization's executive/senior leadership has to adopt a servant-leader attitude and respect that the best decisions are made by the people doing the work.  Transparency of information is critical because if you do not give people the right information, you can't expect them to do the right thing when it comes to work.  People today want to have a sense of ownership and being part of the solution.  The old days of top down management does not lend to this.  However, there are companies, there are people that like the old styles and can thrive. In fact if your organization realizes that is how they operate, it can achieve some level of agility.  They may not be as agile as other companies but they could be agile enough for their own desires. 

The risk level is not the same for all.  What you see as a high risk might be an acceptable level of risk for me.  The key is that everyone involved is able to agree on what is acceptable.  In most cases the executives of a company will establish acceptable levels of risk that the company can take and still thrive.  If the executives are risk adverse then the individual teams will be limited in the risks that they can take. But in the end, the teams have to know that they own their decisions and the risks associated to them while the executives honor those decisions. 

Organizational change does not happen if it doesn't come from, and isn't enforced by, leadership.

So what is your opinion, should the management decide which methods should be applied, the PO or really the whole team?

I'd suggest that the starting point isn't to decide what methods ought to be used, but rather what problems need to be solved, and how complex they are.

Scrum says the core of the organisation is the self-organising team.

The self-organising team - without leaving what scrum.org has to say at all - would get to at least choose between scrum, and scrum with kanban.

A set of teams working together would determine collectively to use nexus - or not - trying to impose scaling on a team that insists on it's own product not working within a scaling framework is not going to work.

But at the end of the day "management" can get rid of a "team" if the team isn't contributing to a real goal. I'd hope the first port of call for this would be via the product owner?

If your whole organisation works with agile methods and only one team decides something else, then it won't work.

At its simplest, this might be resolved by a conversation, which results in a shared understanding about what's important.

But ultimately, the following questions might become relevant:

• Who is funding this team?
• What are the team accountable for?
• What happens if the team are unable to account in a way that justifies further investment?