EVs use hybrid braking, not 100% regenerative. They will fall back on traditional brakes when the required deceleration exceeds regenerative capacity (due to rapid braking, full battery, etc). It reduces the problem, but I'm not sure about "pretty much solved".
You are right about the fact EVs still use break pads but in normal circumstances it is absolutely minimal.
Source: I drive an Audi e-tron and see (in the dash) and feel / hear when the normal breaks are used. Only below 10KM/h and with emergency breaking. The scenario battery 100% full is a pipe dream :)
