The biggest & possibly only one advantage of owning a dedicated home charger vs using the Lucid supplied charger, is iIt frees up the supplied charger for emergencies, road trips, etc ... It's like insurance. Simple.
If you are super disciplined, unlike me, you will remember to take it with you when you pack for long trips & unpack it when you are back home & keep your car charged to 50% to 80% daily.
Everything else, relating to Wifi, SOC limits, etc are all bonus points. Now, if / when Lucid makes available their dedicated home charger, that is a value add, especially if you see power cuts in your part of the country. You can reverse the connection & power your home (but yes, you lose the ability to drive your car for extended distances thereafter.).
Hope the above helps.
P.S: Check with your local state EV incentives. Buying/installing an EV outlet and/or charger will qualify for rebates/incentives.