Digital Signature Algorithm for large files - bottle-necked by hash function? I am new to studying digital signatures like ECDSA and EdDSA, and was curious about something.

Lets say hypothetically I want to create a digital signatures of millions of files, with a total size of 10TB.

From what I understand, digital signature algorithms are hash-then-sign, and the hash functions used must be cryptographic hashes such as SHA-2 or SHA-3. However, looking up the typical benchmarks of SHA-2 and SHA-3, their speed in terms of throughput (bytes/second) seem to be well under 500MB/s per core on modern laptop CPUs, which is not bad.

But in environments without hardware acceleration, it is probably at least 4x slower. On mobile devices, SHA-3 seems to perform 20MB/s on my phone according to a javascript benchmark.

It seems like in certain environments, the hash function will be the bottleneck in both creating the signature, as well as verifying it. Especially for mobile devices -- it would take several days to sign/verify a 10TB inventory of files.

Are there any cryptographically secure digital signature algorithms that are optimized for large files in terms of throughput? Or are we always bottlenecked by the hash function?

Are there any fast, non-cryptographic hash function we could use for digital signatures while keeping the cryptographic security?
It is potentially a bottleneck, but will it be a problem in practice?  My phone doesn't have 10TB of storage, and if the files are remote the network speed will be the limiting factor.  There are other strategies possible, like computing hashes as the data is transferred to the device, or hash trees for updating a hash without re-computing the whole thing (for e.g. a small edit to a file).