Is this an artifact of current network dynamics or is it explicit in the protocol?
In other words, can I, today, send zero-fee transactions and reasonably (99.99% of the time or something) expect them to be processed by some _known_ deadline? (Be it 24 hours or a week or whatever)
It is just current network dynamics. Confirmation times in general are unknown as blocks are produced on an arbitrary timescale that the software attempts to trend to a 10 minute average by actively changing the difficulty of the proof-of-work mechanism to match the entire hash power of the network.
For transactions without fees there is no way to guarantee anything.