The urgency was faked and less true of the Manhattan Project than it is of AGI safety. There was no nuclear weapons race; once it became clear that Germany had no chance of building atomic bombs, several scientists left the MP in protest, saying it was unnecessary and dangerous. However, the race to develop AGI is very real, and we also have no way of knowing how close anyone is to reaching it.
Likewise, the target dates were pretty meaningless. There was no race, and the atomic bombs weren't necessary to end the war with Japan either. (It can't be said with certainty one way or the other, but there's pretty strong evidence that their existence was not the decisive factor in surrender.)
Public ownership and accountability are also pretty odd things to say! Congress didn't even know about the Manhattan Project. Even Truman didn't know for a long time. Sure, it was run by employees of the government and funded by the government, but it was a secret project with far less public input than any US-based private AI companies today.