Most git objects are tiny files, so internal tree-based parallelization won't bring much compared to file parallelization (git is a hash tree itself, with variable-length leaves).
SHA256 is actually a lot faster on modern CPUs due to https://en.wikipedia.org/wiki/Intel_SHA_extensions (and similar on Arm), which are implemented for SHA-256 but not for SHA-512, e.g. openssl speed sha256 sha512 on M1:
Hashing is not the only thing that stops git from being useful for large file versioning. For this purpose, splitting files into chunks using a rolling hash (similar to how git packs, rsync, tarsnap or IPFS) would work better. This again doesn't require "internal" tree hashing, since each chunk would be hashed separately.
SHA256 is actually a lot faster on modern CPUs due to https://en.wikipedia.org/wiki/Intel_SHA_extensions (and similar on Arm), which are implemented for SHA-256 but not for SHA-512, e.g. openssl speed sha256 sha512 on M1: