Robin,
I'm finding it easier to name courses that dont have a footpath, or track or road that is used by the public!
A few more that do, not yet mentioned I don't think:
Hunstanton (across the 8th and 9th to the beach)
Brora (specifically path from the caravan site to the beach)
Virtually all the course I can think of in Derbyshire!
A few that don't think have paths?:
Brancaster (probably due to the thin spit of land not being crossed, though people perhaps wander up into the dunes form the beach?)
Littlestone (dont remember any and cant see any on the link below)
Notts and Coxmoor (perhaps the coal mine landscape when they formed wasn't conducive to a nice walk in the countryside?)
If you want to check any specific examples, try this website:
http://footpathmaps.com/Adam's example of the 10th at St Enodoc was a real pain when I played there some years ago. Plenty of walkers on the path, perhaps more making the trip to Betjeman's grave at the church? The significant thing for me is that the path runs parallel with the hole (well down the middle of it!). Those that run perpendicular to the line of play, such as at Burnham, work better as its easy for golfers and walkers to get out of each others way quickly. As for those in public access areas like commons and parks, well...
Cheers,
James