That’s probably true, but I doubt he would accept it. He’s looking for something bigger. He’s looking for something to bolster his national profile, that he can use as a stepping stone to bigger things, after Trump. Press Secretary, influential though it may be, is not high status enough for him. He’d essentially be a salaried employee whose sole job description would be to defend the Trump administration. Not a good look for someone whose agenda is to build his own brand. He wants a cabinet position with managerial powers, to demonstrate his prowess (if it exists).
You seem to be pretty close to Vivek and got all the inside dope on his plans for the future.