Which kind of wrens? House wrens, I’m guessing, or Carolina?
It’s interesting how differently we can view the birds. Here wrens are fine. They build their own nests in spots where the bluebirds can’t fit. The holes are a little smaller, I think.
Besides the House Sparrows, our Bluebirds have to deal with food competition from Starlings, and Cowbirds like to lay eggs in Bluebird Cardinal, and Wren nests.
Nature can be very cruel.
House wrens. Have not seen a Carolina wren I don’t think they come to Michigan. House wrens are nasty birds. Famous for destroying other birds nests, easting of kicking out eggs, and and nesting is any old spot, like an open rural mailboxes. They also are aggressive and will dive at peoples heads, even eyes.
WE are fortunate in the woods here, many small insect eating birds. Rarely see a staring or cowbird and just a few bluejays which are are nasty to open nests.