One of the most iconic shapes of the rapier has a swept, or open hilt, made using an elaborate set of rings.
While the rings could offer some protection compared to nothing, they seem to have a bigger diameter than the rapier blade, and thus wouldn't an opponent's rapier have a significant chance of slipping between the rings and injuring the wearer's hand? Why would a rapier choose the open ring design over the closed cup design, or at least a semi-closed design?
Short version: The way that early rapiers were used meant they didn't require heavy hand protection.
Longer version:
Swinging a sword for an extended period of time is a lot of work, and a large hand guard means you're moving more metal around. Think of it like modern sports or camping equipment, where reducing the weight of your equipment by a few ounces or even grams can mean a big difference.
When the rapier was first being developed, European sword fighting tended to be more focused on cuts and throwing an effective cut requires that the hand to start back and then moved forward. An example of this would be the Guardia Alta stance from Achille Marozzo's Opera Nova published in 1536. Because the sword hand is held back, it's tough for an opponent to target and therefore doesn't need much hand protection.
As fencing evolved over the next hundred years or so, the thrust became more prominent and the sword hand was more likely to be held in a forward guard, such as that shown in Capo Ferro's early 17th century book. This is certainly not to say that cuts disappeared, but they became less common. The full cup hilt was invented for a form of Spanish fencing, La Verdadera Destreza, where the ideal position was to have the sword held at full extension in front of you. The farther forward your sword hand is held, the easier it is to target with a quick thrust and the more hand protection is needed.
The swept and open hilt guards are primarily intended to protect the hand against cuts. That's why they have just a few bars in a pattern that will block the occasional cut but still have openings that a thrust could slip through. As fencing stances shift forward, those openings are gradually closed off and the hilt moves towards a more solid defense. It's also worth noting that this isn't purely a linear evolution. Cuts never entirely go away and rapiers with fairly open guards continued to be used throughout the 17th century. There's also a lot of issues of fashion and personal preference mixed in, and battlefield swords (as opposed to the duels the rapier was intended for) continued to be more cut-focused throughout this period.
