Because if a normal business goes bust leaving customers out of pocket, it’s usually only a small percent of the customers “wealth” (and often insurance will cover it).

If someone’s bank goes bust they can loose a much larger proportion of their wealth. Often causing them to go bust, causing more bankruptcies and job losses.

Governments act as insurer of last resort for most bank defaults, because the confidence of the banking system and money is integral to the countries existence.