You'd be silly to charge your EV with 120v at home, but it's not going to damage the battery, it's just slow. Most EV's actually come with a 120v cord, called a Level 1 charger, so you can do this in a pinch (and so the manufacturer can be assured that every buyer will be able to go home with a charging solution right away).

Your implication that 120v charging could cause permanent damage is completely bullshit; batteries can be damaged by excessive charge rates but not by slow charges.

Nor is 240v a trickle charge. Trickle charging is typically considered just enough to offset self-discharge, which even 1.5 kW Level 1 chargers can exceed. Level 2 240v charging is a "normal" charge, and is generally around 0.1C (a 10-hour charge), which is very safe for most battery chemistries. Level 3 DC fast-charging is the fast option, and the only one that really causes extra wear and tear.