I've never seen this on any boat but the parker. Anyone added pop up cleats? What's the purpose of having the holes through the gunnel down to the cleat? Seems like such an annoyance.
Nominally, it keeps the covering boards free from obstructions, while still allowing you to have a traditional cleat (which are stronger) attached to a structural member on the boat. It's very common on larger sportfishermen.
Replacing them with pop-ups is going to be a bear. First, you're going to need to fill the hole, which will involve a pretty advanced level of glass work. Then, you'll need to gelcoat it to match, which can be tough to do with the nonskid texture. Then, you can install the cleat; make sure to use a backing plate bigger than the size of the repair as I wouldn't trust a patch job with that amount of point loading.
Overall, unless they REALLY annoy you, I'm not sure that's a repair that would be worth it. I'd try to work with them a bit before biting the bullet, maybe they'll grow on you.