I can think of several reasons why it won't happen that don't rely on
conspiracy theories.

I'm not actually evincing a conspiracy theory, merely accepting the reality
that the words Bernard Woolley from (the written version of) "Yes, Minister"
are as true now as they were 20 years ago:

"Every Department acts for the powerful sectional interests with whom
they
have a permanent relationship"

Thus DfT is always going to be more swayed by the (likely) views of service
area operators, who will be known to them, than the motorists, who are an
amorphous mass.

How do you define 'nearest'? As the crow flies; by road; in time taken? I
can see arguments between petrol stations and hotels about who should be
on
the list as nearest.

The signs will need to be kept up-to-date because the last thing someone
running low on fuel needs is to follow the signs off the motorway to a
place
that has shut down.

Also motorway service stations are open 24 hours whereas most non-motorway
petrol stations aren't so opening time information will have to put on the
signs, and this would also have to be kept up-to-date.

Well, if American cousins can manage this, it would be sad if the consensus
was that it was beyond the capabilities of the British :-(