1) Banks are solvent. Assets exceed liabilities. They have a liquidity problem if there is a bank run, but can unwind there position and pay all account holders if given enough time to do so. (To be clear, it is still possible for a bank to go insolvent)
2) Historically, bank failures and bank runs were a major recurring problem. Our current financial regulations are written in the blood of those past failures.
3) Among the many safegaurds in place is the FDIC, which insures depositors against bank failures. The FDIC is backed by the US government.
There are two different failure modes for Teather
1) A liquididy problem (bank run). Teather pauses redemptions while until it is able to liquidate its other assests. Might cause a panic, but long term, your Teathers can still be redeamed for dollars. If their is trust in the market about this, 3rd parties can provide liquidity as a form of arbiteage (causing the value to dip below $1, but not crash)
2) A solvency problem. Tether runs out of money and the remaining holders get 0. Or, Tether knows they haveva problem and pay everyone pennies on the dollar.
People are concerned about failure (2)