How far it migrates only depends on the sat/vB market rate for transactions.
A powerful lot of work being done there, with the word only. If you have an insight into the future of the market rate for transactions, whose inputs are a function of everything going on in the world, you are a vastly smarter man than I.
The reason I’d suggest a miner offering that is because they could pay whatever fee they want to themselves and eat it as part of the course of business.
It seems like you're talking about what amounts to a secondary market layer at work with miners: there's the math of literal on-chain transacting, in which certain UTXOs aren't viable to spend due to dust dynamics; and then there's an overlay market where people pay miners out of band, somehow, to consolidate dust in some systematic way? Is that right?
If so, I've concluded something similar, sans details. It's inevitable, I believe, that btc will be an element (perhaps a principal element) in a larger financial ecology -- it will be a layer, in other words. But there will be other layers, and the interactions between them will be complex, as systems always are. The mining dynamics you describe (or rather, that I am construing you as having described) would be one such potential dynamic.
I am greatly simplifying and reducing the complexity of everything happening in the world that can and will affect Bitcoin to get to the meat of calculating the current market rate for processing transactions. Luckily, the economics at this layer can be reduced to simple supply and demand—even if chaotic elements abound in the greater ecosystem. So while things like Ordinals can add demand, it still reduces the answer to this: the cost of a bitcoin transaction is whatever the market is able and willing to pay for the limited and prioritized space in blocks at any given time.
It’s entirely possible that demand will stay high for a long time, and rates could maintain 50+sat/vB or higher, but there’s a natural redistribution of those fees into consolidated miner payout UTXOs that then get sold into the market and then a reprocessing of those UTXOs by miners to mine blocks (paid for by the market). If the market is unable or unwilling to pay, mempool space clears and fees drop. This has happened several times in the history of mining already.
This does bring up an interesting attack vector though regarding censorship. If a powerhouse like the NSA moved quickly enough before lightning network really gains popularity, they could eat the cost (printed money) to inflate the mempool with high fee transactions in order to choke out smaller paying transactions (weaker currency holders in developing nations). However, this would be quite costly to maintain over time and ultimately I think the market would mitigate high fees with the kind of consolidation market behavior I described. Still fun to think about how a massive nation with imaginary money could try to attack it :)
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Let me put it another way. I believe there may be a scenario where:
  • the demand for block space is really high
  • the cost to transact is therefore really high
  • UTXOs that are now clearly not dust are rendered, by those conditions, into dust
In other words: the market is operating just fine, btc is alive and well, and due to demand for blockspace my $100 in btc is now unspendable except by some potential extra-market mechanisms, as discussed earlier. There's no way for my $100 UTXO to be consolidated because it's un-economical for ant miner to include it, non-chain arrangements notwithstanding.
It seems like you don't think this scenario is possible, but I'm still not making the connection as to why.
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We have reached alignment with one clarification: it could be economical for a miner to include your UTXO if you are willing to spend up to 100% of the chain value as a fee (as we discussed, strange new markets could emerge) :)
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