The citation for contempt and arrest by the House puts Barr in a position where we want him because the DOJ has decided to obstruct an investigation on grounds that never applied to begin with. This forces Barr to go to the SCOTUS and argue something for which there was never a basis. As said above there is no legislative need or intent in question as the law upon which the "shall issue" order is based has zero to do with anything Treasury and the DOJ is claiming. What a shitty prospect for a defense. Meanwhile, Mnuchin can enjoy his historic view from the Congressional holding cell.
Politically I think going after Barr will be difficult.
While a strong majority think Trump is not telling the truth on the Russia matter, it has been highly visible and debated for two years and the camps are highly entrenched. I think there is a real danger of solely focusing on and escalating the Russia matter. We have a pretty strongly formed opinions on whether Trump cheated and obstructed. It's just down to enforcing the penalties at this point.
Otherwise it drowns out everything else going on.
The tax returns have been simmering in the background, but has a significant chance at driving at a totally different Trump narrative (is he a real business success, or just a fraudster.) Plus it can also inform us of Trump's potential motives towards Russia.
Lastly, I think Mnochin is a weak little bitch who will crack in an instant. He came from a career in Hollywood and banking. He's recently married. Presumably he wants to return to that life in the private sector. Disgraced, pigfaced and in cuffs? Tough image to sell yourself on.
Otoh Barr is old AF, a politico, and firmly in a legal career path in it's twilight. Going to prison for Trump may actually win him credibility in certain deplorable circles.
Seeing an unphotogenic mnochin get worked over first may soften the public up for seeing the AG go down, and hopefully cause the AG/DOJ reconsider it's path.