That's a good question. Titles aside, Silvio was closer to Tony and smarter than Paulie, so even though he turned out not quite desirous/capable of the job, it made sense that he would have gotten first whack at it.

I can't remember now but wasn't a rough consensus reached among the leaders at either a wake or a restaurant that Silvio would temporarily step up?

"When the snows fall and the white winds blow, the lone wolf dies but the pack survives."
Winter is Coming

Now this is the Law of the Jungle—as old and as true as the sky; And the wolf that shall keep it may prosper, but the wolf that shall break it must die.
As the creeper that girdles the tree-trunk, the Law runneth forward and back; For the strength of the Pack is the Wolf, and the strength of the Wolf is the Pack.