Are there any good tools to visiually display a product backlog sorted by its priority?

I'm not sure if there's a tool out there that can do this - the tools that I've worked with tend to require some kind of manual ordering. However, in my opinion, this is more consistent with Scrum. The Product Backlog is not sorted by priority, but is ordered. Priority or business value are only two factors to consider. You may also want to consider the availability of experts, dependencies or relatedness of Product Backlog Items, and size when figuring out what the right order of the Product Backlog is. Consider that the order is intended to convey an approximation of when the team will be working on each item. Just because something has a higher priority doesn't mean that it's the next best thing to work on.

There are tools but you will fall into the Tool = Agile mindset and leadership will willingly settle into that because they will be able to pull reports and see who's working on what and who's being productive.

If you have flexibility, why not make the wall your product backlog? Pro tip. Buy "super sticky" post its. Visible to everybody. And if you insist on documentation, use Excel. Tools make life difficult for development teams. But in some cases, you don't have a choice because management paid for it and now you must use it.

Does the Product Owner believe that the only way to order the Product Backlog is by value? Does nothing else have to be taken into account, such as urgency, risk, business cohesion, or technical dependencies? If nothing else seems to matter...why not?

@Phey,

One day maybe they will just be able to plug in the business values and the order will change "AutoMagically"

Is this really more intuitive and useful than changing the order with a drag&drop manually? As Thomas and Ian pointed out, business value is not even the 'single best' attribute for ordering the product backlog.

@Mark,

If you have flexibility, why not make the wall your product backlog? Pro tip. Buy "super sticky" post its. Visible to everybody. 

That flexibility was available in the '90s. It was fading away as reality by 2019 and became history in 2020. A physical wall everyone can see...?

Thanks for your feedback everyone and I agree with all that has been said.  I was referring to business value in the wider sense, not just the value generated by the item, good feedback nonetheless.

We do use the DevOps board as the equivalent "Sticky Note Wall", remote working has made a physical version a little challenging.