Wouldn't that be conflict of interest? The Executive Branch should work separately from the legislative branch, so what if Trump decided he could fire his Secretary of State for one reason or other and try to force the Majority Leader to lead the vote in the senate---or fire his wife. This is just an example, but there could be other problems concerning his wife.
While I agree it is a potential conflict of interest, such conflicts may be unavoidable.
Our Political Class is so insular and interconnected, these sorts of connections are bound to pop up with almost any appointment.
If we want to try to minimize them, I suggest we start with more consequential ones, such as the time Phil Gramm passed a securities trading law called "The Enron Exception" while his wife, Wendy Gramm, was serving on Enron's Board of Directors (with pay, of course).