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Wires are not part of the z-plane ordering and so you cannot put things behind wires. "Send to back" and "Send to front" aren't options when you click on a wire.
Wires already respect z-order with respect to each other, and you can "Move to Front" and "Move to Back" when you select a wire. I think what you're suggesting is that in addition to this behavior, they can also be promoted above other BD objects.
If you want to be able to move wires in front of objects, then this suggested Idea is seemingly predicated by this Idea to ensure wire ends don't awkwardly overlap their sources/sinks.
Sorry I meant more explicitly " In fact there does not seem to be a way to send anything behind wires." to quote the original request. I've seen several requests that decorations, labels and even nodes be put behind wires. I just wanted this idea out in the exchange for discussion.
Labels and decorations is a somewhat viable request. Moving in front of nodes is not without significant change to the connection behaviors of nodes in LabVIEW (including but not limited to the change that Jack mentioned regarding wire connection points within nodes).
Any idea that has not received any kudos within a year after posting will be automatically declined.