You're not making the point you think you are.

Anisogamy also refers to some plant sex characterizitions; its a paraphylitic group. Its better to think of it like a basket you can sort things into.

There's also evidence animals have transitioned between zw and xy sexual systems multiple times. Its likely that in transition periods there would be both zw and xy which suggests historically, at least a kind of transitory "xyz" system (which would fall outside anisogamy's definition if x y and z all had different sized gametes - not an impossibility) where there were likely two compatible pairings and a noncompatible pairing but that would be a costly system to maintain so its not surprising existing observations don't see this occuring.

If such things were identified in the wild it could be defined as a "third sex" or as a "transitory sexual system" etc. Dolly the sheep also had 3 parent/donor cells instead of the usual two. Its a special case but it also falls outside of normal sexual reproduction model as many gene editing expiriments do.

The models describe commonalities, not certainties or absolutes. This is why the original analogy is fine; there are things that seem like they would obviously fit into sexual reproduction (>1 but not exactly 2 dna donors or parent organisms such as polyspermy) but we still call it a binary because such instances are rare. The original analogy is also an obvious analogy for gender (or "legal sex" or "sex assigned at birth" because as soon as it has a social context it becomes gender and law is a social context).