There's a general problem I had to encounter unfortunately (independent of paralleled batteries):...
The problem comes to if it will shut down immediately or cause damage before it shuts down to the second BMS and that's the part I don't know and truthfully the Chinese manufacturers probably don't know either
...
When charging my batteries with a solar MPPT charger and the (last) BMS decided to switch off because the battery was fully charged, there had been a voltage spike destroying my inverter input circuitry.
My thesis is as follows:
As the MPPT charger is a buck converter, it consists of at least one heavy inductor. And an inductor doesn't like to be switched off when in full swing. If it is nevertheless, this leads to VERY high voltages (this effect had been used effectively for decades in car ignition systems). On the bright side, I can report that no BMS ever gave in (even not the ones that already had switched off).
So as a result I now make sure that the solar charger switches off below the BMS "trigger" voltage, i.e. the solar charger "Over voltage disconnect" has to be lower than the "sum volt high level 2" entry in the DALY software.
Furthermore make sure, there is no inductor somewhere in your setup (remember a coiled up surplus cable is already an inductor).
Coming back to switching off BMS under heavily load: As an inverter also uses inductors, it also might not like radical changes in current. But this holds true also for system using just a single battery.
So I have to agree with ericfx1984 and ereams65 ... BMS manufacturers just go on the safe side because they probably didn't went through the effort of testing it.