Lilo, there is no narrative explanation about why Vito tapped Luca (as opposed to anyone else) to infiltrate the Tattaglias/Sollozzo. It must all be inferred. However, the novel states that, on the Don's order, Luca had initiated contact with the T/S several months before the attempt on Vito. So, if Vito is shot a week or two before Christmas, then Luca made his first contact when? - mid-September. Of course, Vito sending Luca was a big mistake since the novel makes clear that Luca's allegiance to Vito was legend and that legend would have been well known in the underworld community. That community's members would be the last to accept Luca's claim of dissatisfaction with the Corleones.

Your comments about Vito's political connections evaporating upon his death confirm my hypothesis about Barzini. Barzini didn't care about securing Vito's political and legal connections - Barzini wanted the big seat, so he let Sollozzo and the Tattaglias do his dirty work.