Verifying just the total supply misses the point. Bitcoin’s power is that every satoshi can be traced back to Genesis and the initial creation of each, and each block proves conservation at the moment of transformation. To measure this you need both the number of UTXOs and their relative amounts vs a changing total supply. Encrypting amounts hides those relationships. You can check the end total, but you can’t verify that conservation held across the chain, nor measure the entropy each block resolved from Genesis onward. That breaks Bitcoin as a thermodynamic measurement device and re-introduces trust, turning it from an auditable process into a black box.