There will be very little dynamic load tapering on single phase AC charging because the charging power/rate is so low. Even on a 7kW system,which tends to be the maximum power rating of a single phase OBC, that is, relative to the battery of a modern EV, trivial to handle (where the battery is rated to deal with hundreds of kW during useage). Hence, connect the EVSE, the car signals its presence, the EVSE closes it's contactors, and the OBC will pretty much straight away ramp to the requested charge current and hold that untill 100% SoC is reached in most cases (or the OBC charge scheduler otherwise terminates the charging). Even with a hot/cold battery, just 7kW is unlikely to cause an issue with cell balancing or cell thermal effects.
Once you get to dc fast charging, at powers between 50 and 250 kW then yes, the real time dynamic capability of the battery cells starts to matter, and charge rates will vary with SoC for example