Here is my bit for product brainstorming. Below, I call the rebasing token YAM, yet I do not propose this for YAM design. I just think it is an interesting direction for elastic finance.
In the current design of elastic finance, rebase reallocates value from the price to quantity/supply. I suggest we iterate on the idea of allocating it (partially and after user opt-in) elsewhere. For example, this can be a token mint or a deposit to some sort of a vault.
I will give an example of such a mechanism - a stable coin yamUSD. I have 1 YAM and its price is $3. Normally, rebase would give me 3 YAMs at $1price. Instead, here (suppose, deposited in a designated contract) I get, say, 2 YAMs at $1 and 1yamUSD worth $1. While I assume YAM price fluctuates to some extent. yamUSD should always maintain a $1 price. How? Well, we know that at every rebase 1YAM=$1. Hence, 1 yamUSD can be redeemed for 1YAM at/after every rebase, so you always get $1 worth.
You like the example? Sorry to disappoint, there is a major issue. If the price of YAM decreases before the redemption, this introduces inflation to the protocol that could trigger further price decrease and collapse. In fact, the whole protocol would be one big Maker CDP and, obviously, it can get liquidated. Perhaps, if there were issuance limits and the treasury served as collateral of last resort, it could somehow work.
Anyway, the point I am trying to illustrate is that with normal coins it is unnatural to have discrete frictions that would be predictable, so it seems wrong to make a cut and extract value from the protocol at some arbitrary point in time. YAM rebase is a predictable recurring event plus the fact that 1YAM = $1 at the rebase is an incredibly powerful property. That could allow for a fluid value extraction during positive rebases. Also, the value loss due to value reallocation will be not as pronounced in nominal terms due to elastic supply. In the example above, we went from 1YAM to 2YAMs, and that in real terms (and standard denomination) is equivalent to a $3 to $2 decrease.
I am curious to hear any thoughts on this. At this point, I do not know how to take the idea anywhere further, though I believe there could be some potential.