A Positive and Hopeful Sign in the Banking Crisis• https://www.fff.org by Jacob G. Hornberger
The purpose of the assurances was to discourage people from withdrawing or transfering their deposits from smaller, regional banks.
An article at CNN Business this past Saturday pointed out that despite those repeated assurances, "Deposits at small US banks dropped by a record amount following the collapse of Silicon Valley Bank on March 10, data released on Friday by the Federal Reserve showed. Deposits at small banks fell $119 billion to $5.46 trillion in the week ended March 15, which was more than twice the previous record drop and the biggest decline as a percent of overall deposits since the week ended March 16, 2007."
In other words, many American depositors obviously did not believe all those assurances about the "soundness and resiliency" of the banking system. They obviously believed that U.S. officials could be lying to them. They didn't want to take a chance on that possibility and lose their money.