The CBDC is beyond a payment innovation facing customers. What it really changes is the lending relationships between big financial institutions (wholesale) and customers (retail). Let us say you hold some retail CBDC, it will be a central bank's liability, instead of a commercial bank's liability.

One may ask how this changes anything. Consider the old financial arrangements under Bretton Woods, where the "strongest" money is gold and SDR, they back the US dollar. The US dollar in turn backs other currencies. These other currencies back commercial bank deposits, and commercial bank deposits back financial securities... Therefore, regarding safety, you have gold > cash > deposit > securities. Regarding liquidity (in a narrow sense), you have gold < cash < deposit < securities. One explanation to the crash of the Bretton Woods system is Triffin's Dilemma, where you have basically a constant level of gold and SDR, but the amount of US dollar was continuously going. So in the late 70s, there was a run on the US Federal Reserve (Fed), and the Fed was unable to meet its gold obligations.

Obviously, during monetary expansion and when the economy is doing well, there is no difference between cash (CBDC) and deposits. It is always more profitable to hold bonds, given that they do not default. However, during crisis, banks may go bust and runs are frequent, so people would prefer cash. If the crisis becomes even bigger and the central bank might go bust, people would prefer gold (or bitcoin, but this remains to be tested), as seen in war times.

Since there is currently no crisis, why do financial authorities think of CBDC? The reason can be explained on multiple fronts. First, since the 2008 crisis, it is realized by financial regulators that credit expansion needs to be tackled while it is growing instead of after the crash happens. This gives rise to the ideas of macroprudential policy, and the CBDC is thought to have multiple use cases here, for example, easier helicopter money, and more supervisory power for the central bank on commercial banks. Two, there is a lemming effect between governments. China's former central bank governor, Xiaochuan Zhou, was very optimistic towards CBDCs, as it was thought to be able to benefit the internationalization of the Chinese Yuan. After China developed its CBDC, many other countries followed suit... If you think of other reasons, feel free to comment.