It is regeneration that unites us to the nature of Jesus. Jesus being righteous imparts new God-life from His own nature to us, and God is satisfied.
In that sense, the idea of the transfer of guilt is accurate. But we carry the concept too far until it becomes a plainly mechanical thing, like a commercial transaction. There must be a vital, living commitment.
Righteousness is imparted to the believing sinner who is united to Christ. It is not imparted to the sinner who simply stands outside and receives a judicial notification that he has been "made righteous."
This adds some important light. As believers, we are accepted in the beloved Son. We can never be accepted out of the beloved Son.