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].)
It doesn't because they primes are not multiplied together in ECC they are added to the generator point that many times which precludes trying to factorizate of a public key in the first place (you'll just get a bunch of meaningless factors that have traces of G and the private key in them).
Are primes handled "better" (whatever that means) when for example signing transactions, resulting in better byte economy for the blockchain?
I think you mean whether they can be computed the fastest, which the answer is no. The points which can be generated the quickest are powers of two by means of repeated point doubling.
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.
That's around 2^248.53, but it could be larger depending on how OP is generating them. That's because it is computationally impractical to test whether a number is exactly prime so instead people use algorithms that test if they are "probable primes" such as if (a
n-1 mod n) === 1 for some a between 1 and n, however although these tests pass for all prime numbers they also pass for a small proportion of composite numbers with huge factors.