As a practical matter, SCP's asymptotic security follows from the fact that it depends only on digital signatures (and hash functions) for security, and that these can be tuned to resist arbitrarily powerful attackers.
For example, you consider an attack in which every grain of sand on earth is a supercomputer attempting to break SCP a billion times per second, and you decide you'd like the expected time required for such an attack to succeed to be over 100 years. Then that means you need roughly 128-bit security, so you choose cryptographic key lengths and hash function sizes accordingly. (Note that for public key algorithms you generally need longer than 128-bit keys for 128-bit security.)
The more powerful an attacker you want to resist, the longer your cryptographic keys and the slower your operations. But the important point is that the cost of running the protocol increases far more slowly than the cost of attacking it, so you can basically adapt to an arbitrarily powerful attacker.
In Proof-of-Work, the cost of running the protocol is the same as the cost of attacking the protocol, so you cannot resist an arbitrarily powerful attacker. Instead PoW generally adds an additional incentive structure (mining fees) and then assumes a rational attacker. In Stellar's case, those incentives are not good enough because Stellar allows tokens other than XLM to be traded, so even if Stellar did provide some kind of mining reward denominated in XLM, the reward might not be valuable enough to deter attacks on other assets. (Financial networks send around trillions of dollars a day, which is more than even the Bitcoin market cap.)
