In practice, you still need the museum's cooperation to do anything commercial with it, for most people who don't have the resources to defend a lawsuit.

More importantly, even though you can't copyright a photo/scan of a public domain work you also don't have to share those images with others at all, you could still paywall them off and (arguably) impose additional restrictions as a condition of getting access, and you certainly don't have to host the files online for everyone like this.

Yes, you could physically and contractually prohibit others from copying the original work.

Could you though? Once you have a good image if it isn't copyrighted it sounds like any licencing agreement is void. You could just distribute not under terms of the license, but as a public domain images.

Wikipedia has assumed, since Bridgeman vs. Corel, that images of public domain works are public domain. Once some portrait museum in the UK threatened to sue, but backed down quickly.