You still need one hash for every non-leaf node, so 30-40 hashes of 256 bits each. What this algorithm saves is 30-40 indices, which is 11 bits each for a 1000-leaf tree. Even aligning to 16 bits it's doesn't seem a great optimization.

Unless I misunderstood something and we are not trying to minimize the size of whole proof, but just its structure - but I see no reason why it could be useful. But I can see there are two other papers: one on distributed Bloom filters [1] and the other on Bloom trees [2], maybe these can shed some light on it, I'll check later today.

[1] https://arxiv.org/pdf/1910.07782.pdf

[2] https://arxiv.org/pdf/2002.03057.pdf

EDIT: I haven't noticed you are one of the authors! I liked the paper, it is very clear and visualizes how Merkle (multi)proofs work in a nice way. The only thing that worries me is claim of significant reduce in the size without providing any hard data in that topic.