I suppsoe in part it is to do with the consequences.
If I get a ringer in to pass my driving test, I am then able to drive with a licence in my name that I did not earn. I would be breaking the law, and a potential danger.
If I get a ringer in to take my music grade exam - the only loss or risk is to myself. The main risk as mentioned is that of exposing myself subsequently (as it were

) For example, if I audition somewhere brandishing my G8 distinction certificate when I am blatantly unable to tell which end of the instrument to blow (an even bigger deal if it's not a wind instrument

)
The only exams I've had to produce ID at are my OU exams. That I can understand, as with distance learning the OU wants to be sure that the qualifications it awards as 'legitimate as possible'. While each assignment is signed to say it is all the work of the candidate, only in the exam will there be definitive proof of that (let's face it, someone who gets someone else to write their essays might just be willing to lie and sign saying it was their own work)
At school exams we didn't have to produce ID but then the teachers knew who we all were! At full-time uni, didn't have to produce any ID there either. I suppose the chance of finding a ringer to take 24 hours of exams for you - on which your entire degree rested (no coursework) - was pretty unlikely!!