The BMS balances during charging only. Almost always, it does so by draining current from full cells/banks during charging. Most BMSs are made down to a price, and so they can only drain current slowly, maybe 100mA, and so the whole battery charge rate has to be dropped to the drain rate so that full cells are not being topped up faster than they are being drained.
I explained that, during testing, my BMS was unreliable. That seems like an excellent reason not to trust it to me. I have seen it not work very well.
There is an excellent Youtube channel devoted to exposing the horrifically unsafe devices coming out of China on EBay etc. Un-earthed shower heaters, USB charger with mains exposed on the casings, exploding LEDs, etc. Those Chinese product designers do precisely what you say they don't do - they save a few pence at the expense of safety. And I have bought lots of devices from China which were faulty or whose advertising was complete rubbish. And I've faced devious sellers when I've complained. So I don't know why you assume they must all be well-motivated, highly-qualified engineers. Some undoubtedly will be, but that doesn't mean everything coming from China is top notch. I don't need to think I know better than the best to be generally cautious.
And I know that Lithium Ion batteries are inherently more dangerous. That is precisely why I don't want to put a £7 BMS permanently in charge of a big battery unattended.
As far as I know (assumption 1) , a Lithium Ion battery which is not being charged or discharged is safe as long as it isn't heated way up or mechanically assaulted. When it's charging it's on a balance charger which has numerous safety features and I'm attending it. It sits next to me in my office. When I'm riding it, it's discharging. It currently doesn't get hot in use and I don't allow it to over-discharge. As far as I know (assumption 2), worst case is that a cell fails short circuit, and that might cause very high currents. There are three fuses protecting the battery, but if for some reason they do not blow or do not stop thermal runaway, then overheating, and a very energetic event might occur. I believe that that likelihood is very small, as is that of a car accident or a heart attack. And that low probability should be factored into making a reasonable choice. But if it happens, I'll be on the bike, and outside. I'll be aware that something is wrong quickly, and I can get off the bike and take appropriate action.
Of course, it's not always possible to know what you don't know, and perhaps my assumptions are wrong, but they are not faith-based - I've looked into this quite a bit. But perhaps there is another terrifying failure mechanism I'm unaware of but I have not learned of it here.