pull down to refresh

As a TL;DR, we came up with two alternative protocols for Ark, which have the following properties:
“Erk”: no user interactivity for rounds offline refresh (server can refresh for a user) perpetual offline refresh (server can keep refreshing for a user indefinitely) works best with single input and single output vtxo requires CTV + CSFS
“hArk”: no user interactivity for rounds very efficient, also for multiple inputs no offline refresh possible (so far) requires CTV only
According to 2ndbtc, "Using Ark will inevitably require ongoing costs to maintain a balance." Is that the case for Erk and hArk, or is it specific to covenantless Ark?
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