With a variant wire typing Get Variant Attribute and selected pressing Ctrl+I inserts the SubVI with the variant wire through the "Default Value" and "Value" terminals.
I'd have expected it across "Variant" and "Duplicate Variant"?
I was able to reproduce this behavior, both with Quick Drop, and with a standard right-click Insert operation. I have filed CAR 509902 against the Insert feature, since Quick Drop doesn't currently do any custom processing of the inserted object, and getting the method fixed would also solve the right-click Insert case as well.
Set Variant Attribute and Delete Variant Attribute work ok. I'm guessing Get Variant Attribute is causing a problem because the type checking code for the terminals is starting at the bottom (by default), and the array of variants output is "close enough" to a type match that it goes ahead and wires that up, not realizing that a better match is farther up on the node.
Also, FYI, if you insert Get Variant Attribute on both a variant wire *and* an error wire with the Ctrl-Shift-I shortcut in Quick Drop, it works fine, since that is a completely different codepath than a standard insert.