The rapier hilt is typified by an large ricasso in front of the crossguard. In front of the ricasso are rings, and sometimes a bell or other hilt projections designed primarily to protect the hand.
In the old days, there were various schools of how a rapier should be handled. Some taught "using the rings" others taught gripping the weapon in the middle of the grip, and others taught using the pommel (called "posting" in modern fencing).
I think it's clear that the form of most rapier hilts favors using the rings, and that's where it went. The Classic Italian grip (shown below on a foil), clearly shows the rapier heritage.
The Belgian also shows some of that heritage (more so than some of the other orthopedic fencing grips).
Rather than trying to explain it, I've rather quickly sketched over the pictures to show that heritage, if you squint a little. You can also see it in the shot of me holding the Italian grip.
The rapier was not to be swung like a saber, but you could slash with it. Using the rings gave a lot of control and power, as does using a grip like the Belgian--- which is the highly developed offspring of this approach.
There is nothing weak about these grip, though it is true they are less suited for hacking than a straight grip.
Regarding the parry: The strength of a parry is determined by position more than any thing else, including the relative weight of your blade. You could have a heavy saber and try to parry with the end of your blade (The foible) and you would be ineffective. You could parry with the middle, and might be marginally effective if you're strong. If you parry with the forte--the area just in front of your guard you will be effective even if you're a small woman with a thin little sword. There's no substitute for leverage.
You could parry a heavy saber with an epee fitted with a modern grip. It's not ideal, but neither is attacking an epee with a heavy saber swing. You'd be in real danger of getting transfixed while your arm in the air. The smart epeeist wouldn't even take the parry, but that's tactics and another discussion.
(Sorry for the long post

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