Having the charger in-car is really not a convenience, it imposes multiple limitations. on BEVs.
Where kW rates are available at the charge site at higher rates than the on-board charger, the slower onboard charger is only a bottleneck preventing faster charging. It often prevents the desirable kW rate for any BEV/BEVx/PHEV at any charge site, which is either the maximum the grid infrastructure at that location supports, and (far less frequently) the maximum the battery will accept (~48 kW for A ~24 kW pack like the LEAF's) both subject to kW cost/rate considerations.
An on-board charger can not be used to charge other BEVs/BEVxs/PHEVs (yours, or other drivers') while you are not using it, making its use extremely costly and inefficient, by requiring us to collectively pay for many more chargers than are necessary to service all BEVs public charging requirements.
An on-board charger adds large additional costs, weight an complexity to BEVs/BEVxs/PHEVs, and almost all of them probably will have to be thrown away, after the rest of each BEV/BEVx/PHEV reaches the end of its useful life.
An on-board charger will never allow vehicle-to-grid or vehicle-to-home kW transfer, which a two-way DC device will be able to, which can add additional value to the significant investment (the bigger the pack, the greater the benefit) every BEV/BEVx/PHEV owner has made in their battery pack, and in the case of BEVxs and PHEVs, add value to their on-board ICE as well.
The "waste" heat produced from the on-board charger is not recoverable, while, if the on-site charger is properly located, this heat can be recovered to meet the needs of the human passenger's activities, while they are charging.
As I mentioned before, before the transition to on-site chargers is complete, you may want to carry a portable charger with you, especially when driving in remote areas.
At some point in the future though, I expect that notion will probably seam about as quaint as carrying your own fuel pump and hose with you, just in case the gas station you are headed to doesn't have any fuel pumps on-site...