As far as I can tell, the fans are currently screaming that they should have taken Darnold and that they gave him away to the Jets. In my scenario, they'd have had an extra pick as well. In fact, given how the draft panned out my suggestion would have been exactly the right thing for them to do, given they took Barkley anyway.
I don't disagree with you. And if they really were determined to take Barkley no matter what, they should've traded with the Jets to get that extra pick, as you said.
That doesn't change the reasoning why they didn't/wouldn't. If they had traded with the Jets, no one would've believed them that they always intended on taking Barkley, and everyone would be pissed they gave away Darnold to the Jets. Of course it's irrational, given how it played out anyway, but a large part of fandom is the irrationality of it.