The scanning process may interfere with the ability of other members of the public to enjoy the work in the usual way.

The scanning process may damage the object in some small way, which could accumulate over the course of multiple scans.

The queue for making volume scans may be packed with amateurs, who will make low-quality scans, with limited distribution. These might prevent the timely creation of a high-quality scan.

So it is really in the interest of the public to allow the most competent scanner to jump the queue, make the best possible scan with available technology, and distribute that to everyone who wanted a scan in lieu of allowing them to make their own.

If a work of art is removed from exhibit once every decade or so for a new scan that is better than the last scan, and that is distributed libre to any visitor that wants a copy, there is no argument to be made for anyone to make another scan, unless it can add information that is not already in the existing files. For instance, if the usual scan relies on reflected visible light, a magnetic scan or transmitted light could reveal other information, such as perhaps a previous image that was painted over.

obviously within regulations. But the museum should have no right to deny access after setting up specific appoinments with approved scanners.

Do you also feel this way about photos?

Which do you mean? Photos of a museum piece or photos as the exhibited work?

For the latter, if the photos were taken on film, reproduction prints could be made in the same fashion as the exhibited print, and any scanning should take place using the negatives. On-plate photography is more appropriately digitized using a scanning machine, rather than with a handheld photographic camera.

As for taking pictures of a museum piece, as long as you are no more disruptive than someone using their eyeballs, I have no problem with taking photographs, even if the displayed work is still under copyright. A blanket ban on photography puts an unfair burden on the photographer to prove fair use a priori. If there is a problem with copyright, the work in question can always be blurred or blacked out with digital editing, leaving the remainder of the photo intact.

But I don't believe any public museum can ethically prevent visitors from using recording devices of any kind unless they provide libre digital copies of the protected work that are objectively better than anything that could be produced by an amateur in situ.

So by all means, charge 8000 euro for a volume-printed reproduction of the bust. But if you want to prevent people from "scanning" the original, you had best make the high-resolution scan the museum already possesses available for download first.