I love Who as much as most in this thread, been to conventions, bought products etc, watched most of the episodes both old and new series alike.
I think the main issues for a falling popularity are
Every episode seems to be based on earth, what happened to planet xyz and spacestation 123, we have a whole universe / multiverse and the whole of existance to make stories with, but each week we have London, Birmingham or some other part of the world of the 21st century.
In the 70’s and 80’s the Doctor did visit earth but no where near as much as now.
I know that CGI isnt cheap, but digital filters on film to change the sky or colour of plants is cheap and easy, its school kid easy, as it can be done post production with shop bought software.
The wastelands of Skaro were filmed in a quarry near where I used to live, we went there as kids after filming had wrapped, although my parents didn't tell us at the time. 7year old me found Skaro oddly familiar the next week.
When I worked at IBM the building I worked in had been used many times for filming for different episodes none of which were earth based.
They used a disused MOD airbase near me for one of Colin Bakers encounters with the Daleks prior to it being demolished and turned into a housing estate.
I think what I am trying to say is they used to be more inventive set wise and managed more with less.
Nowadays with time travel a mainstream plot device in most sci-fi and some dramas they need to make more effort in my opinion. As nothing they do is ground breaking.
We have good story writers but average scripts most of the time, with the occasional excellent one in the mix.
The BBC wont can it yet as the merch still sells and they have way to much invested, but as its publicly owned, sooner or later if ratings go down questions will get asked.
Then the only option might be overseas investment and or a buy off by one of the independent UK channels.
If that happens foreign syndication might be more difficult, Auntie Beeb has a massive amount of clout arround the world, and it may end up on a media outlet thats not accessible to the whole of the UK as is current with BBC1 being its output channel. Then it could simply fade away and get dropped.
I hope not as my little boy is just starting to take notice of the Whoverse.