How is abandoned stake functionally different from burned stake or stake in long term cold storage?
If stake is abandoned (or the keys are lost), the public does not know
this fact. They have to account for some non-zero probability that the stake is not abandoned. If the stake is burned, the public knows with certainty that the stake isn't coming back (unless the stakeholders intentionally choose to further dilute BTS to create more stake of equal quantity). When trying to estimate the supply in the future with stake that is burned, one must only estimate the probability that stakeholders will inflate (and by how much). When trying to estimate the supply in the future with stake that is abandoned, one must incorporate the aforementioned probability in their calculations as well as the additional probability that the stake may not be abandoned.
I am not saying this is a big deal or anything. I am just stating my preference that I would prefer the extra certainty.
One thing I should mention that is far more important though is that if we ever want a proposal voting system in which a certain percentage of stake quorum is necessary for things to happen, we would need to be careful about picking the right denominator. Do we include all stake that exists on the blockchain including stake that are abandoned, or do we choose the sum of the stake that has only moved in the last year, for example. So as long as we appropriately take that into account in any future proposal systems that depend on certain percentage thresholds, I don't care too much if stake expiration is never implemented (which I guess has some marketing benefits).