I've heard that Bitcoin will finish mining in 2140, which is certainly a long way off.
A long way to go, that is right. With a view linke today, it takes 2 human lives to do it, if you take the average age of death. That annoys me again and again when i read it, i like to look at the development after the halvings and look forward to the months after that... maybe which we are all looking to

I think the transaction fees will be so high after 2140 that the miners will continue and find a solution to be effective and profitable. With the reduction of miners, the hashrate will be lower and they can calculate the blocks with fewer miners. So there is a real chance.