Why would a central bank want a national digital currency?

According to the IMF, the key reason developed economies consider a national digital currency is to counter the growth of private forms of digital money. The demand for low-cost, convenient digital payments is rising, and the government sees this as an opportunity to get in this market. Digital currencies have the potential to make it easier, cheaper, and faster to move money around.
With cash more and more disappearing, disruptive apps and fin-techs are experiencing larger payment volumes, raising concerns about consumer protection, data privacy, and operational risks. Policymakers are therefore pushed to explore a digital currency solution before users commit fully to adopting alternatives that have very limited government control. Economists have also argued that central bank digital currencies can improve market functioning.
The Bank for International Settlements (BIS) has stated that it can improve liquidity by allowing faster transaction speeds, and the Bank of England noted that it can boost GDP by up to 3% by lowering transaction costs.
Additionally, in more emerging economies, national digital currencies are primarily being considered as a means to increase financial inclusion because they allow governments to include unbanked populations in the digital economy.

Sven Franssen