The older the garment, the more formal it tends to be, as witness the robes worn for ceremonies in Academia that predate the the advent of tailored clothing. And when it comes to shirt cuffs, in case you were wondering, the single layer link cuff style worn by Gabriele d'Annunzio in the photograph is the oldest of them all, dating back to the time when buttonless shirts were pulled over the head. Not coincidentally, as the only acceptable cuff for use on a shirt to be worn with a tailcoat, the link cuff is also the most formal cuff style.
We are today used to French, or turnback style cuffs, with a double layer of fabic. Despite their ubiquity however, turnbacks are a relatively new innovation. So far as I know, they were introduced by the late Duke of Windsor when he was Prince of Wales and rebelling against starch in his evening dress. There is no way to wear an unstarched single cuff with cufflinks, but a turnback can be worn soft. So he did, with his double breasted dinner jackets and other innovations. And so now do the majority of the rest of us when we choose to wear cufflinks.
Given their history as evening wear it should come as no suprise that the vast majority of the link cuffed shirts extant are white, but link cuffed shirts can be worn in any situation where a white, cufflinked cuff shirt is appropriate (note that linked cuffs are not the same as convertible cuffs, which do not have the thicker interlining required to provide the linked cuff's required stiffness). It is a cleaner look, completely appropriate, and with the small added advantage that few men other than the wearer will be wearing it. That latter point of course makes it yet another collectible for the dedicated.
Adding link cuffs to the shirt wardrobe presents a couple of small challenges. Chain-linked cufflinks as worn by Mr. d'Annunzio tend to be too long, allowing the linked cuff to gape open. Lighter weight stirrup or snap links work better, which may come as a potentially expensive surprise to the man who does not already own a pair.
The other obstacle between linked cuffs and your wrists is likely to be whether your shirtmaker offers them in the first place. The construction as I have said is different internally from run of the mill cuffs, and not every maker will have had cause to figure out a design. But surely a small batch of three white linked cuff shirts from someone who does know how to make them is a minor barrier.
Consider the oldest cuff.