Assumes lognormal prices, constant volatility, no transaction costs, continuous trading and a constant rate. Every one of those is false.
Why it survives anyway. It is used as a quoting convention, not as a belief: it maps price to a single interpretable parameter invertibly, which makes options comparable. The wrongness is absorbed by letting implied volatility vary by strike and expiry.
The deep insight is not the formula but the replication argument - the option is hedgeable, so its price is determined by no-arbitrage and the real-world drift never appears.