The 1987 stock market crash did not leave much lasting impact on the economy, but if these liquidity problems had been allowed to cause the default of a major clearing member or even a CCP then it could have had a much more serious impact.
While this might seem like simply an interesting bit of history, the payments chains involved in central clearing are still very similar today. To guard against the same sorts of liquidity risk today, we need to make sure that every link in these chains will work as it is intended to under stress.