I hope there is no bad thing happen to binance, it seems that if binance is collapse then it will become really bad sentiments for bicoin market. Although the market will recover again but it might affect the public trust, I realy hope that people out there don't hear any bad news about criptocurrency.
It is not about public trust in my honest opinion, so many centralized exchanges have collapsed or have been hacked both in older and recent events, anyone of the public who pays even the smallest attention to crypto should be aware of these, and know then that any exchange can collapse. They operate with a fractional reserve system, so they can quickly become insolvent if something goes wrong for them. The only thing that can affect public trust towards BTC is a successful attack on its network, which is almost impossible to happen.
There is an impact to BTC price if binance falls down, since its one of the top exchange in the market, and also there are lots of traders who uses bitcoin, having million transactions daily and binance close that is a big blow, but at the moment that is a bit hard to happen, Zhao had already prepare for this a long time ago that is why he is in Dubai, the us government putting pressure on him, made this move, because he knows what will happen.
You are one of those who believe in cz that funds are SaFu, and they are too big to fail, take note that no exchange is too big to fail, and if you have your money stored there, you should move it into self custody.