The national governments should perhaps worry about this.
A corporate currency would be tied to the corporations products. So and Exxon “Petro” or Amazon “Booker” would, in effect have an intrinsic value based upon the value of the product being marketed because corporations could not issue more of the currency than could be redeemed for the products they provide.
That would make them safer currencies in many ways.
Everything old is new etc. Until the 1930s most paper money in Canada was issued by private banks; the two largest banks here continued to issue notes until 1944.