I believe this issue is pre-dated even further, back when iPod users didn't like that occasionally a random shuffle would play the same song back-to-back. So the 'random' shuffle was made a bit less random.
A shuffle already implies shuffling like a deck of cards, so you wouldn’t get duplicates unless you had two of the same card, and I that’s how it was described in the manual.
You don't need to make it less random to achieve that. A 100% random shuffle won't have that issue, you just have to make sure it's actually a shuffle and not something else.
I'm going to ignore the other ways to handle that and just point out that that is multiple shuffles and won't be a problem if the user initiates all shuffles.
If the user has to initiate all shuffles, it won't play continuously. If you handle it another way, that demonstrates that it doesn't "just" work with a pure shuffle without using those tricks.
A non-uniform probability distribution is still a probability distribution, and, as long as it doesn’t assign probability 1 to any particular outcome, is still “random”.
A shuffle already implies shuffling like a deck of cards, so you wouldn’t get duplicates unless you had two of the same card, and I that’s how it was described in the manual.