@Nissim: You do not need to
@Nissim: You do not need to install a new charging system. You didn't describe what your existing charging cable is. If it's J1772, a $50 J1772 to Tesla adapter works great.
@Salesoft: The reason for leaving the car plugged in is two-fold: first to keep the main battery at a good level. Second, to maintain the 12v battery. It may seem counter-intuitive, but the main battery doesn't recharge the 12v battery. That protects the 12v system from draining the main pack to low and damaging it. If you don't leave it plugged in, the 12v battery will die sooner.
Another reason to leave the car plugged in is for emergencies. What if you need to drive further unexpectedly? What if you end up in the hospital and the car is unplugged for weeks? There's no good reason NOT to leave it plugged in. The battery doesn't need to be held at 50%. It can be held at 70-90% without problems. It's only a problem when it's held at 100% for long durations.
Similarly, letting it drop to 10% isn't a good idea either. Low state of charge accelerates lithium ion degradation. If possible, keep it above 30%.
What you are doing right is charging at low rates. "Low" is relative to the size of the pack. With the large packs that Teslas have, even 40A L2 charging is "low".