But does it have any actual use? I'd love your take on it.
No.
Does it add value? (Primes cannot - by definition - be factorized, so no one could ever arrive at your private key by factorization and multiplication [if that's even a thing].)
I don't think that's a thing. All the methods that solve ECDLP are working with the public key which I haven't seen be affected by whether or not the key is prime.
Are primes handled "better" (whatever that means) when for example signing transactions, resulting in better byte economy for the blockchain?
It won't affect anything in signatures unless you also brute force the ephemeral key for signing and use a custom one which would significantly decrease the security of the signature. It also doesn't change anything regarding size of the signature.
Is this unsafe? (I think not, according to the
prime number theorem (PNT) there should be about 6.54*10^74 primes - a huge number - in the range as defined by the secp256k1 with the ECDSA algorithm. In other words, of all possible private keys, approximately 0.056% are prime, but only a few of these correspond to public addresses whose hash160 happen to be prime too.)
It is slightly less safe since the search space is being reduced. I have to study how prime-counting functions work more before I can say anymore.