> In Monero, the adversary can refine their guess of the distribution based on the inputs that are actually mixed in, and that is what creates the privacy weakness.

That is not what is claimed in Section 4 of the paper. Section 4 merely indicates that of potential outputs, the time distribution introduces a bias toward the most recent (actually in Monero this might be inaccurate in some cases too: very, very recent might be less likely than merely very recent; the paper does not examine this). In Zerocash the same time distribution bias exists, though across a larger set of potential coins (or notes or whatever it is you call it).

However, very old members of that set are essentially irrelevant as their probability in the distribution is almost certainly extremely low (this is the same reason that more older outputs in Monero are essentially irrelevant).

It's the same claim as for semantically secure encryption, for example: no competent cryptographer would claim that encrypting a message implies that the adversary's knowledge of the plaintext distribution is uniform; only that the ciphertext gives the attacker no further information (apart from length, typically) about the distribution.

It is, in the same sense that the first order anonymity set of Monero transactions is all outputs included in the ring signature which can't be proven implausible (e.g. using the methods in Section 3 of the paper). However, Section 4 of the paper points out that a non-uniform distribution means this is reduced, in practice, to a smaller effective degree. The same method can be used with Zcash to estimate a smaller effective degree since many previous shielded transactions are probabilistically unlikely.

This is certainly not 'deanonymization' or 'tracing' or any such thing, but it isn't that in the Monero case either.