if a single stock can damage the entire system - perhaps it is the system that's not well designed?
People have speculated that this is an area of application for distributed ledger technology, but the Australian Stock Exchange has been trying to roll out such a system and it has been slow: https://www.fintechfutures.com/2020/07/australian-securities...
Trading in securities with daily settlement, while movement of money is not operating on the same frequency, means that there is a requirement for someone to take that risk.
That's the systemic risk, not the trading itself. If the execution, settlement, and clearing of a trade were simultaneous and instantaneous, then there's no risk to the market itself.