You're generating a random number (the UUID) then you're hashing it. It can't possibly have more entropy, and there's a chance two inputs to the hash will collide thus reducing entropy.

Hashing a counter is actually a variety of CSPRNG. Basically you're re-seeding a hash-based PRNG with whatever PRNG the UUID code uses at each run. It's well known that an PRNG cannot have more entropy than its seed. Hence, it will at best have the same entropy, and probably have slightly less.