The three rings were not destroyed, they just lost their power.
I hardly doubt that they would be able to make them again, or make another set.
Celebrinbor, the maker was dead and nobody in Middle Earth had his skills, he was second only to Feanor, and I suspect that even Celebrinbor maybe wouldn't have been able to reproduce his work (taking what was said by Feanor and Yavanna that for there are some works that can only be done once).
The question of why the three were bound to the one ring is a good one, and it has no answer.
the three weren't made by Sauron, he never even touched them, and apparently, the relation between the three and the one wasn't known even by the wise.
During the Elrond council, Gloin asked what would happened with the elves rings if the one was destroyed and Elrond said he didn't know that he thought they would lose their power, but he didn't know for sure.
All I can think, and this is my own idea as I haven't read anywhere is that even being very different in power, malice and objectives, the elves, ring, the one ring and all the other ring were in essentially the same, worked the same way.
The three were not made by Sauron, but Celebrinbor used his own skills enhanced for what he learned from Sauron. So, even though Sauron never touched them, he knew about their making, he knew how they worked and somehow, he could master the one ring to control them, using his superior skills and power.
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