Just because someone has an image that is in the public domain doesn't mean they're obligated to share it with you. They can simply say no. Your options are:
1. Hire a photographer to take a photo of the artwork that you want to use. You have to pay the photographer, and you still need the museum's permission to access the work in a setting where you can take a good photo suitable for publication. You probably can't just snap a photo while touring the museum and use that.
2. Use a photo that the museum has and pay them and/or agree to their terms. Maybe you could take that photo and then share it because it's technically public domain, but guess what's going to happen the next time you want to use one of their photos then?
Well, they can't say no if you are already in possession of the image.
Certainly, they are under no obligation to take the photo, deliver the photo, host the photo on a server, but once you have the photo, there is no legal mechanism from preventing you from using it. Your arguments in this thread have gone: copyright protects photos of public domain works -> well people can still sue you -> well people don't have to give you access. You have arrived at the truth: museums don't have to take photos or share them with you. They own the physical artwork and can control physical access to it. I don't think that was in dispute.
It’s a moot point that you can use it without permission if you can’t obtain it without permission. This is a distinction without a difference.
That’s why it’s actually a big deal and a Good Thing that museums are making these images available online. It’s not as simple as “they were public domain anyway”.
1. Hire a photographer to take a photo of the artwork that you want to use. You have to pay the photographer, and you still need the museum's permission to access the work in a setting where you can take a good photo suitable for publication. You probably can't just snap a photo while touring the museum and use that.
2. Use a photo that the museum has and pay them and/or agree to their terms. Maybe you could take that photo and then share it because it's technically public domain, but guess what's going to happen the next time you want to use one of their photos then?