if your basing it on moving 1btc... the answer is naturally when it becomes costly to the point of over 1% (so 0.01btc fee) to move it people will lose preferential desire to hold bitcoin.
I disagree. People will see an incentive to hold bitcoin as long as the price keeps going to the moon. If the fee is 0.01 BTC, but the price of 1 BTC is $10,000 with prospects of going $100,000 BTC, then who is the idiot that doesn't want to hold that?
As long as the price keeps going up and the fees allow you to move your wealth when needed, it will have an incentive to be the holder's coin.
If the fee becomes higher than 99% of people's wealth and only billionaires see a point in using it, well that's a problem, everyone else will have dumped and only a few will be using it (and I don't see how it can survive in this state, since barely any transaction volume would be going on for miners to be worth mining)
You have an incomplete mathematical conceptualization.
You can't just analyze from the perspective of a percentage fee, because the blocksize is constrained.
It can become possible that transacting in morsels as small as 1 BTC is no longer possible.
So let me get this straight.
Even people holding millions of dollars worth of bitcoin, will see their bitcoins trapped because transaction fees will be worth millions of dollars? What fees are we talking about by 2030? (at supposedly around $500k price)
Well we can estimate given that BTC trades 1/100th of its market cap daily.
So @ $500k per BTC thus a $10 trillion market cap, thus $100 billion transacted daily. Given 144 blocks per day, that is $600 million per block.
Let's assume that whales will put complex settlement transactions on the blockchain with many inputs and outputs so perhaps only 100 transactions per block. Presuming that whales are willing to pay 0.1% fee for security (i.e. $600,000 per block),
that means a minimum transaction fee of $6000. If whales are willing to pay more for security, say 1%, then minimum transaction fee of $60,000.
However, I think whales will end up demanding a kickback from miners for their transaction fees, so that miners can jack up fees on non-whales. Whales can make this demand because they can refuse to send their transactions to miners which won't deal. Yet non-whales can't make a credible threat, because miners who generally offered lower fees would end up losing hashrate relative to those miners who didn't defect from the fee market. Thus I think you will probably see miners colluding to extract the maximum fees that gouge non-whales.
So perhaps 10% fees so $600,000 per transaction. You'll pay it because you have no choice, whereas the whales will have exempted themselves from the fee. So in other words, we will be paying the fees for the whales, eventually the millionaires paying exorbitant fees in order to transact unregulated.
You'll of course be able to avoid that exorbitant fees by going through a regulated option as I explained previously.
So the bottom line is the whales will be free from regulation and we will not. We remain slaves.