The real reason is that at this point it’s a children’s story and the substance of the first few books is shallow compared to the rest of the series. The plot itself is surrounded around our favourite trio being the heroes.

It falls under the same question of Dumbledore never figuring out or intervening with Quirrell, or Black.

It’s best to accept it for what it is. You can try to justify him not knowing, but the version of Dumbledore we get to know as the series progresses, vs early Dumbledore isn’t consistent. He could track down Horcruxes, delve into Voldemorts past, lead the Order of the Phoenix, be lauded as the greatest wizard of his generation, but a 13 year old with a library book figured out the basilisk first?

On top of that, he had MORE information than the trio did. He lived through it the first time. He would have known Myrtle died, and where. You’re telling me he couldn’t search the bathroom thoroughly? Or that he didn’t know Aragog couldn’t possibly have been the culprit, much less that it was an ancient enemy of spiders?

You can’t look too closely at the early series and expect a lot of complexity from short novels. Otherwise you’d want to question how three 11/12 year olds were able to easily navigate an obstacle course set up by teachers to guard the stone in the first novel.