Wait - The Chamber of Secrets could only be opened by an heir of Slytherin. Voldemort or Harry didn't exactly have kids till Harry's final year, who could have come and opened the Chambers.
When Ron opened the Chambers, I don't believe what is told to us - that he had heard Harry speak Paseltongue [edited] while Harry opened the locket and so Ron memorized it. Firstly, memorizing is not Ron's cup of tea. Secondly, doing something that doesn't bother him is against Ron's characterization and I don't see why he would be interested in learning Paseltongue. Finally, I have a separate theory of my own - we know that all the pure-blood families are inter-connected. I know for one, a Black was married to a Weasley. So maybe, some ancestor of the Black in question or of the Weasley, was a direct descendent of Salazar Slytherin. Since all the Weasleys were brought up the Gryffindor way - to value courage and bravery more, the Slytherin bit in them was supressed or even extinct. This characteristic was present in Ron and it is also evident from the time when Ron wears the locket. He is impacted by it more than anyone else and by his behaviour then, I would surely think him to be in Slytherin than any other house. What if, the Slytherin trait was always in him? What if, Paseltongue was more natural to him than he thought? He might have heard Harry speak the phrase sometime but when he was there in front of the snake at the entrance to the chamber, he knew what to speak. .... But this is just a theory. However, the first three points are pretty relevant.
Further, Dumbledore, Hagrid and Snape are the only people who would be interested. Dumbledore never trusted himself with power. The Chamber would have contained a lot more than just a Basilisk. Going there, would mean access to a lot of old relics and maybe magic. Hagrid - well all he would have cared was to give the Basilisk a tender sounding name and then a proper burial. Unfortunately, no one else would have wanted anything similar. For Severus, the word 'mudblood' was related to the Chambers and to a sore spot in his memories. He wouldn't venture that. Also, after Voldemort killed Lily, I don't see why Severus would want to see of other gruesome ways Voldemort could employ to kill people. All these people, were driven by emotion more than power. They had their emotional reasons to remain away. Someone like Voldemort, who didn't know love, would have tried. But then, he was sort of less-than-a-soul for a while and then in hiding. Any other person, didn't really care, as long as the Basilisk was dead forever.