I was expecting the charger to do that in itself.
The biggest thing here is *when* it comes back on. For example, let's use a 1s battery voltage range.
Fully charged is 3.6V, and during discharge, you do not want the charger to kick back on when the cell hits 3.5V, even 3.4V might be too high still. This is considered "Floating" and could actually damage the cell chemistry drastically reducing its lifespan.
So in a 4s configuration, this would 14.0V for full, and 13.6V. This is waaay too close. Basically the charger would be hammering the battery constantly as lithium chemistry voltages can bounce pretty quickly. It's not unnatural for a lithium cell to drop 1-2% after "fully charged" as it settles. And then it levels out and won't drop any further. Lead acid doesn't do this quite the same and actually "needs" the over charging (aka charging to 14.5-15V for a "12V" system (which is actually 13.5V)). Lithium based batteries can't handle that
So you would need to make absolutely sure that the charger you keep connected won't hammer the battery just because it dropped 1-2% charge voltage.
A "real" LiFePO4 charger actually would monitor the input
and output flow so that it only kicked on when charge "capacity" dropped by a certain percentage,
not the voltage. LiFePO4 does not have a linear discharge curve like LiMN or LiCO (the other lithium cells usually 18650's etc).
So a constantly connected charger might only kick on/off based on voltage only and this would inevitably kill the cells sooner