You will not use 110V for home charging, you will use 14-50 32 Amp charging, and it will easily charge overnight.
Just like you, taking the charger with me was my original thinking back in 2015. My installing electrician set me straight-I returned my wall charger. All you need to take with you is the J1772 adapter for some public chargers. The only time I take my charger with me is on long trips, where there is a small chance I will need to use a 110V or an RV park for 14-50. That is less needed now that there is such a prolific Supercharger network. In my four, over 4,000 mile road trips, I needed it twice, and could have gotten by with alternatives.
Trust me---you will rarely, if ever, unplug and take the included charger with you. For the price of the wall charger, you could purchase a back up mobile charger, and still save money on the wall charger install.