there's only a small amount of unmined BTC left, approximately 1,100,000. While the number currently mined is 19,900,000, there's still time to accumulate BTC.
That's a weird way of putting it! As if you are suggesting that without a block subsidy, people won't be able to accumulate bitcoin! Which may be the reason for your follow up question.
Trading bitcoin (and people accumulating it) takes place on the market and is unrelated to mining and its reward. People buy and sell bitcoin from and to each other on the market. Any coin you buy from an exchange today is many "hops" from a coinbase reward. Which means in the future without a block reward, the market should not change at all. People will still continue trading with each other with the coins they have.
The only thing that changes is when "supply" of fresh coins entering the market/circulation decreases while "demand" goes up, the price should go higher. Which is one of the reasons why we usually have a big bull market each 4 years starting after the halving (supply cut by 50%).
I like the way you try to throw more light by separating the idea of individuals accumulating bitcoin from the mining subsidy. That seems to be the part were many people misunderstand everything and tend to tie those two together. As if bitcoin cannot be sold or bought unless it is mined. Anyone expecting bitcoin adoption to slow down or get stopped is delusional, as they do not know how liquid the bitcoin network is and how much the value will be in the future.
So, what Op is more concerned is if people can still buy bitcoin without a subsidy, right! and also how humans behaviors can evolve due to a shift from an era of insurance to a system driven purely by fees. And you are totally right there, everything falls down to incentives, for buyers, sellers and miners too, in fact to everyone using the network to make transactions or validate one. The moment new coins dries out in the supply chain, miners will be left with fees only.
So yeah, the average man buying bitcoin won’t care if their sats came from a 2025 coinbase or a 2011 cold wallet. But the bigger question, which OP seems to be against (even if awkwardly), is whether the overall ecosystem’s game theory holds up under no-subsidy conditions. This includes the incentive for new entrants, the robustness of the fee market, and whether in the future accumulation might end up priced out by excessive competition for blockspace.