If he doesn't sign wih the Bengals he will have to sit out and rejoin the draft next year likely as a 2nd or 3rd round pick. Meaning he gets much less. That is not going to happen.
I just find it hard to believe Burrow would suddenly drop that far in one season. It's not like he suddenly becomes a worse player because he sat out a season. He'd get drafted in the top half of the first round next draft, if not higher. He'll still be a top 2 or 3 qb next draft imo.