Antonio Brown's cap hit the next 3 seasons

He is not getting a new contract while effectively making $20 million per season. That does not make any sense. Nobody with any common sense is rumoring that he is trying to get a new contract and no team in the NFL is going to pay him $20 million a year while he is still getting $5 million a year from the Steelers. The Steelers bad decisions do not effect what he does with his new team. People really need to stop making up crazy rumors on here that have no merit.
I disagree. You are simply disregarding what you don't want to consider. High profile player getting traded wants a new deal. Every. Damn. Time.

And someone will give it to him.

It won't be us, thankfully. So you can stop peddling the 'certainty' of Brown's cap figure, because his current deal will either be up in smoke when he dons a new uniform, or (less likely) he'll be in kiss and make up mode in Pittsburgh, again while chasing a new contract.