I don't see our current FO moving up for Burrow, so I do not consider him available to us for QB.
I don't see Tua available for the draft yet. We will know about that after this coming Monday. If he does opt for the draft, which is in no way a sure thing, I don't think out FO will take a chance on him.
We do have enough draft picks that taking a chance is not unreasonable. I just feel that our FO (you know, the only ones whose opinions mater in who we draft) will focus their picks to the other areas of the team that need help.
I do not think they feel our QB situation is the biggest weakness we have. I would like to see them pick a QB, but not until the end of the draft. That way we focus our higher draft picks to areas where we are the weakest.
By picking a QB near the end of the draft, they would still be adding competition to the QB position with potentially viable QB candidates. We could also wait and try and get a UDFA QB, But the availability of potential QB's falls off quickly in the draft and I doubt that the FO considers UDFA's a useful area to find QB's.