The Wall Connector used to cost $1,200, then dropped to $750, now is only $500 or $550 depending on cable length. It is really a no brainer to install a hard wired EVSE to charge your Tesla. The Mobile Connector should be exactly what its title suggest, to be used when you are mobile. I use mine at my in-laws, 120V charging at hotels when I can, etc. 90% of my charging is either at a J1772 station at work, or my Wall Connector in my garage.
So basically, if you are having the amps reduced with your Mobile Connector, you might want to consider installing a Wall Connector.