The mystique certainly adds flavour. Here in Australia it is not as big an issue and to a much lesser extent, as they are much more accessible generally (with two notable exceptions)
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I still think it depends on the merit of the courses, here there are courses that have merit, are private, but not highly ranked.
In the States, I am sure there are many that are very inaccessible but are also not highly ranked?
So is it possible, that these learned men of the early parts of last century and more, knew from the beginning, the early stages, what gems were being created and made sure they would be locked down to keep them exclusive, not ‘spoiled’ by too much traffic.
In turn, this takes a different angle, that the exclusivity has no relation to a courses rank, it just maintains a different perspective for those that love GCA.
The Old course has no such restrictions, but has buckets of intangible aspects that make it very special as well as the golf. As do many of the courses in GB&I and here in Australia.
My answer would be a YES – for most of the list you supplied – they would still be great and considered the best, no matter how easy they were to access.
BM