> I don't understand this. First, AFAIK unilateral exit in DryjaPoon always has 2 txs (otherwise you wouldn't have punishment), not one.
It is two transactions to punish, yes, but if no punishment is required it’s only one. You then have an on-chain UTXO that can be spent like any other (and only by you), even though it isn’t a totally normal P2WPKH output.
> Secondly, I'm assuming an economic push towards cooperating users just evicting non cooperative ones, so it's not even always 2 tx per "wallet", but potentially even as low as 2*logN/N txs, in optimistic cases where users just migrate to another ark where the current one is unresponsive. I know this is not how it works now, but I'm speaking about the potential evolution where high fees may push the system.
An Ark can only be exited on-chain in one of two ways (and I’m not aware of any designs that would materially change this) - either the operator after a timeout or unrolling (at least part of[1]) the tree on-chain. Yes, you can roll your vTXO over inside the Ark system, but that just means the operator claims, and depends on collaboration with the operator [2]. If the operator is gone, you pay to dump the whole tree on chain, which is, basically, two transactions per user [3]. With a tree structure you can’t do better.
[1] in theory each branch of an Ark tree could allow the operator to step in again, allowing one user to leave without forcing the entire unroll, but there’s still just two options for each leaf.
[2] okay, you could trade your old-Ark vTXO for some new-Ark vTXO if the old-Ark operator went out of business, but now the new-Ark operator has to pay to unwind your old-Ark vTXO so you’re not getting out of the unwinding cost.
[3] in case it’s not obvious, if you could all the intermediate nodes in a tree, you get N-1 (the second to last layer is N/2, the next layer up N/4…to 1, which sums to N-1). Yes I know you can make it an N-ary tree and reduce raw transaction count but you aren’t saving on output count.