I'd imagine part of the issue is how difficult it is to stop people from taking photos. Museums and galleries don't want you to photograph some exhibits for the reasons above (copyright and the damage flashguns can cause). However, there's no way you're going to explain to people what can and can't be photographed as you're bound to get some people trying to photograph one thing because they can see someone else allowed to photograph something else. It is far more practical to just have a blanket ban, especially in cases where some exhibits can be damaged by flash. I think the person working in the museum was probably being quite lenient and allowing you to take photos if you're not influencing others, but there's only so long people can turn a blind eye.
Weston Park Museum seems to have a fairly flexible attitude towards photography. Anything delicate or copyright seems to be grouped together in one gallery, so with the exception of that gallery I think you're allowed to photograph anything. This should make managing the museum easier and should make it easier to teach kids a bit of museum etiquette. Limiting the 'no photos' area to a gallery of a certain nature should help demonstrate why you can't take photos in most galleries. I don't think kids would learn anything from a blanket photo ban over the whole museum.
I think quite a few museums and galleries probably have certain non-gallery spaces which you're allowed to photograph. Am I right in thinking the cutlery dragon in the Millenium Galleries is in the corridor? That's still technically part of the museum, just not in the exhibition rooms so I guess you're allowed to take photos.
I never understand why museums, galleries, stately homes etc. don't wise up to people wanting to take photos and make it clear in guide books etc. what postcards are available of what you're looking at. Extortionately priced places like Chatsworth and Blenheim ought to offer a few postcards for free as part of the entry price. It'd save museum staff a lot of hassle, would give people a better experience visiting somewhere as they'd be able to enjoy just being there rather than feeling they have to surreptitiously take photos (or be jostled out of the way by someone else trying to do the same) and the photos would be heaps better than any that people can manage on their own camera.