The real problem facing these models, as with most of the wonderful objects interned behind the scenes in our national museums; the museums are given so many objects, many small and seemingly uninteresting, some large and or dangerous and thus undisplayable. This puts them in the predicament mentioned by the curator above that they have to choose carefully what is relevant and interesting, easy to interpret by the general public and tie in with the museum's overall theme.
The ship models are a case in point; the curator would like to display these models, however, as Colin has said they simply don't attract the majority of the public's imagination. This now means they must go into storage to allow the museum to display things which do attract the public- this is how museums survive after all! Imagine how upsetting it would be if the LSM closed and no-one wanted to take responsibility for the models...
As for the fear that the models may fall foul of that most Briitish of institutions, namely beaurocracy; let me assure you that once an object, any object enters a museum it is the most difficult thing you could imagine to remove it- rember that most are given to the museum with a caveat 'this was my father's.grandfather's mother's/grandmother's flim flam jibbety wacket and it simply MUST be looked after for the benefit of the education of future generations!', this is all documented upon entering the object into the museum's itinerary and provides huge amounts of information for anyone thinking 'why is that in the museum...!', as well as the all important provenance of each object- it's reason for being kept and taking up valuable space.
The way many large museums are trying to go, led by the NRM in many ways; is to display the stores as part of the museum, in humidicly controlled storage buildings that are safe and accessable to the general public. Perhaps in the future the LSM may try to go this route too.
Interesting that the Barrow Dock museum be mentioned for their displaying the wonderful Vicker's models there- if you take a trip to Furness General Hospital, you will find a collection of large scale ship models of a calibre that would make museums drool with envy and they are on display to a captive audience (well, until your cured/healed/annoyed and leave...) seen by hundreds of people every year.