Um, no you're not. The Crucible was designed by the other races that the Reapers harvested, not by the Reapers, and it was built by the current set of species.
And honestly, I don't see how it matters what you use to stop the Reapers. Being trapped by Reaper tech is regarded as a bad thing because it's something the Reapers exploit - a weakness to any civilization that does it, mostly coming in the form of the Citadel and their surprise attack using it, the Mass Relays keeping the expansion of each rising organic race to certain areas for the Reapers' convenience, and the Reapers' understanding of the tech being inherently vastly superior to the organic races using it, making it easier for them to fight it. If the Reapers are stopped, using Reaper tech ceases to be an issue (unless you're using Husk or Indoctrination stuff, but then your problem is moral issues, not practical ones).
Because they have no choice. They know just enough about the Crucible to know it's designed to stop the Reapers, and seems capable of generating enough power to do so. Given that they know they have no way to win conventionally, going with a device they don't fully understand but have reason to believe could win things for them is certainly better than the alternatives. It offers them hope where they'd otherwise have none, if nothing else.
Zevox