Rustle, you make an interesting point about motorway service stations. Your analogy isn't perfect (either) because you're talking about something you never pay for (pulling up to use the toilet at the service station), whereas a precautionary landing is a version of something you do normally pay for.
No, of course I don't go to the GP with a rumbling stomach even if it's free, but if the GP happened to be in Edinburgh when the festival is on and they provided free transportation from my home in London perhaps I'd be more likely to find myself with a stomach ache each September. So free landings for true emergencies might not be misused, but if your "heard a funny noise" arrangement allowed one to avoid landing fees at what may well have been your intended destination (who is to know?) then I'd be surprised if it wasn't abused. I wonder how "soft" the reason for a precautionary landing could be at one of the many fields which have signed up? "Southend Approach, G-ABCD inbound, but only to use your loo"???!
And as for utilising a service that is sitting there idle anyway I can't agree. Do British Rail (or whoever owns the trains these days) give away free seats on their trains, just because the incremental cost of accomodating you is zero?