Here, I would like to defend Vito. The move was not as stupid as it looks from the end of the story. Luca's mission was not to play the betrayal of his Don but to play a guy who is a little uncomfortable with the family and his income. I think Luca played his role well. He doesn't agree on the deal too quickly. It takes him months until he gets in contact with Sol.
I think, sending Luca was smart. But Vito couldn't have thought that Luca got killed as soon as he touched Sol's hand. Killing Luca only made sense because it was embedded in a larger move: Making Paulie switch sides, killing Vito, kidnapping Tom. Four moves at a time. It was a risky thing. And unlike Michael a couple of years later, Sol failed. Vito survived twice, and Sol got killed in the end.
A guy like Solozzo was too bold. Too bold for Vito. Too bold for himself.
Vito's mistake was that he didn't see Barzini behind all these things