but Fauci is not an economist

He isn’t thinking that way (about economics).

He doesn’t seem to look much outside that lens

Carlson is saying that Fauci is not an economist.  Nothing here to suggest that Carlson thinks Fauci should put on an economist hat and advise the President accordingly. 

can’t see that because he doesn’t think it’s his job to see it. But even a doctor should be able to think beyond the model.

This is perhaps the only sentence in the entire 9:00 min segment where you could insinuate that Carlson thinks Fauci should try to be aware of the consequences of his recommendations.  However, I'm not sure you can justifiably respond to the whole segment with "Fauci shouldn't be responsible for being an economist."  Seemed to me that the larger point of the entire segment was that the President has lots of advisors and he should be listening less to Fauci and more to advisors who know about how policies are affecting the economy.

I agree that Carlson takes a bit of a swipe at Fauci for using the word "inconvinient" when describing the effects of this shutdown on the economy, but I honestly didn't notice it when I first saw the segment and I'm sure even Fauci would use a different word if he could do the interview over again.  Regardless, I'm not sure what Carlson's swipe at Fauci has to do with whether Carlson was saying that Fauci should be responsible for being an economist.  I think it just shows that Carlson thought it was a poor choice of words.  

“For all his credentials, his experience, his apparent personal decency, Dr Anthony Fauci does not seem to understand any of this and we should never let someone like that run this country”

To me, this screams "President Trump, stop listening so much to Fauci and listen more to your economic advisors."  I don't see how this sentence would support your interpretation that Carlson believes the Fauci should be responsible for being an economist.  

After all this, I actually find it increadibly interesting that we both watched the segment and came away with pretty different understandings of what was being said.  I have to ask though, with your initial subject line being "And we should trust Tucker Carlson?" is there a bit of bias in your interpretation of what he was saying?  I'm pretty indifferent about him and was giving my honest take away.  Could be that I missed what he was trying to convey.