Wouldn't it be profitable to make an ASIC capable of calculating private keys? Just looking at vanitygen-plus (currently supporting almost one-hundred crypto-currencies) do its stuff, and it is capable of over 548,990 keys/sec on my CPU alone.

Well developed ASIC is several orders of magnitude faster than my CPU, wouldn't it be profitable for a company with the resources to do so to develop such a key miner, even if it is a one-off?

The reward (actually, theft) is access to the private keys of any address. Surely the development costs are not so prohibitive for ASIC as they are for general-purpose CPU's?

Future developments in this area seem like the most realistic threat to crypto-currency security so far.
You could in theory build an ASIC to brute force private keys of any cryptographic scheme, like EC or RSA. 

But ASICs only give linear improvements. That means that they 'accelerate' some search only by a constant factor, like 2, 3 or 100. Even if your ASIC does something a million times faster than a normal CPU, it's still a linear improvement.

If guessing a private key takes the current age of the universe in a CPU, an ASIC a million times faster would still take 13 thousand years.

Cryptography relies on problems being exponential on the key size. Exponential growth beats linear growth. If some day a powerful ASIC or CPU could guess a ECDSA private key, users of ECDSA would only have to increase their key sizes.

To yield a better than linear improvement, you would need a better algorithm. Implementing current day algorithms in faster hardware only gives linear improvements. It's widely believed, even if we still don't have formal proof, that it's not possible to get better algorithms for prime factorization and elliptic-curve factorization. (At least in non-quantum computers.) In other words, they are considered intractable problems.