OK. We've explained the theory. Let's get back to the OP's request.

He's right.

It's a matter of consistency.

Let's say you start a new song in BIAB. You see that the key is C by default, and the first chord is C by default. You change the key to F by clicking on the Concert Key Signature (to the right of the Style Time Signature). Use the left-hand column. The first chord of the song then becomes F.

OK, BIAB is reinforcing that you changed the key signature by showing a change of that first chord. Choose any of the key possibilities (17, including the enharmonics) in the upper left column and you get the same effect: the first chord becomes the same as the key.

Now choose any of the 17 minor keys in the lower left column. You get the relative major as the first chord. Ex. you see an F chord in the key of Dm.

For consistency, I think the first chord should become the minor key chosen. Choose a key of Dm, and that first chord should be Dm. That behavior would be consistent with what already happens with a major key.

A side benefit is that, as cited, this is a clue (not necessarily a truism, but one of many clues) as to what the key signature of the song may be. It would also reinforce the music theory concept of relative minor key.

BIAB 2024 Win Audiophile. Software: Studio One 6.5 Pro, Swam horns, Acoustica-7, Notion 6; Win 11 Home. Hardware: Intel i9, 32 Gb; Roland Integra-7, Presonus Studio 192, Presonus Faderport 8, Royer 121, Adam Sub8 & Neumann 120 monitors