With the Model 3 in Production Hell right now, I would imagine that adding a hitch is a low priority. Getting the cars our as planned.
First option will be an aftermarket hitch. Later maybe a built in factory hitch as an option. Factory hitch will need to be coordinated with braking, and most likely automatic sway control. Testing in hot and cold weather conditions, beefing up the tires and wheels, braking balance installing proper wiring...lots of things. Not so simple or easy, or it would have come out of the blocks that way.
If you only need it for Home Depot stuff, they usually offer a half day pickup truck rental for $20. Easier than you buying or renting a trailer for those few times you might need it.
See demand for a lightweight hitch to carry bikes, skis, etc, but with the fold down rear seat, most all those things can be carried insided the car when necessary.
On the other hand, I use the hitch on my X quite a bit, so understand why it would be handy on the 3.