Exactly, it's as hard and error prone as generating the randoms yourself. The solution you described requires an analysis of the hash function to determine collision probability, diligence to find a sha-256 implementation (circa a few years ago), review of said implementation, another analysis to figure out your truncation, then a proper implementation resulting in ~the same amount of code, except this time slower and with less entropy.
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.
