This really depends on what they think of Herbert. If they really like him and believe he can be a franchise guy then the trade could easily make sense for the future of the franchise.
Here is the problem/issue. The Bengals front office/ownership has not given fans and players much in the past that would warrant trust in their process. If they would have had a good track record of doing brilliant things then if this happens people would praise him.
The general consensus is that they are a bungling buffoon of a franchise and havent built any collateral trust. The 'safe' move here that buys them time is drafting Burrow. If he flames out then, well, that is more "acceptable" to the fanbase than if they opt to not draft him, wait for Herbert, and flame out with him.
I dont know anything about Herbert so I cannot comment, but if he truly is legit then the bengals could set themselves up for a great 10 year run by trading with Miami.
BUT............... Burrow is the safe/smart move....