That idea works ok for lead acid batteries, but not lithium batteries because their internal resistance is so low. If the resistance is high between one battery and the load (or charging) than the other battery, the battery with the lowest resistance path does all the work until it is completely discharged, then the other battery starts to take over the load.
Unlike lead acid batteries, lithium batteries will hold the same voltage till nearly completely discharged. Balancing between batteries is all about voltage, not state of charge, if one battery has less resistance to the load, that battery will be seen as the highest voltage battery, the other battery will be blocked from sharing the load because it appears as a lower voltage at the load, highest voltage wins every time.
Recharging is the opposite. The battery with the least path of resistance will be seen as the lower voltage and will receive all the charging current until it reaches close to fully charged, then the other battery will start to receive charge ...... the only problem is, the charging voltage where the controller switches from bulk to absorption mode is set at the point the battery is close to fully charged.
This is designed to avoid over charging the lithium batteries, they are glutenous pigs when it comes to being fed and will take in all the current they can get .... right up until they destroy themselves. This is why a lithium charging profile is different to a lead acid charging profile, often the absorption phase is skipped all together and the controller goes straight to float voltage where the last bit of charge trickles in ......
That works great, as long as the voltage is high enough to overcome the resistance to the second battery, but not high enough to damage the first battery due to over charging ..... a very fine line between working well and destroying one battery due to over work because the other battery never reached fully charged and slowly drops further and further behind the first battery ....... Just because the voltage on both batteries read the same, it doesn't mean both batteries are at the same state of charge, the voltage must be a min of 0.5v above the rested voltage for a lithium battery to charge, push that up to 1v if there is an internal BMS because that adds its own resistance between the terminals and the actual cells you are trying to recharge ..... the discharge is the same, 0.5v for a direct connection to the cells and 1v if there is an inbuilt BMS the current must pass through ......
I imagine I've already sent most of you to sleep or to the next post button, so I won't go deeper into the very reasons what might work for a lead acid battery won't work for a lithium battery.
T1 Terry