Cryptographic negligibility has a very specific meaning. Something like a one-way hash function can still be attacked (ie. the original value corresponding to the hashed value can be determined), but it would typically take more power than in the universe to brute-force it. We normally state negligibility on the basis of a computationally bounded adversary, that is to say an adversary who has access to a reasonable amount of processing power regardless of the cost or speciality of the equipment required.

Put more simply: if there is a 0.000000001 chance of deanonymising a transaction that is only around 2^-30. Comparatively, you have a 2^-256 chance of brute-forcing a single Monero output in a single transaction. 2^-30 is not computationally hard, would you trust a site storing your passwords with a 30-bit hash?

To make matters worse: as we get closer to more practical quantum computing we have to consider the effect they will have on cryptography. Anything that depends on discrete logarithm hardness (eg. RSA) is dead in the water, but symmetric encryption and hash resistance will only be weakened, not completely ground up. For symmetric encryption it's "double the speed", so searching through a 2²⁵⁶ keyspace could be done by a quantum computer in 2¹²⁸ time, so symmetric encryption strength would halve. For one-way hash functions (which cryptocurrencies are deeply reliant on) there's a similar speed up for hash preimage attacks (from 2ⁿ -> 2^n/2) and collision resistance (from 2^n/2 -> 2^n/3). So basically take your "possibility of success" and halve it.