Those that want fast confirmation of their transaction therefore increase their transaction fee to get into the next block.
Do the mining programs automatically select the transactions with the highest fees? Been looking at BFGMiner but didn't notice a configuration for this or any mention of it in the README.
The transactions with lower fees are then left waiting a VERY long time to confirm. Eventually, people that aren't willing to wait abandon the Bitcoin blockchain and use some other method for making their transactions. Those other methods may or may not Bitcoin off-chain transactions (such as Lightning Network or Account based services like Coinbase)
Just been reading some very worrying articles about very high bitcoin transaction fees:
...meaning no-one is going to use it to buy coffee or pizza. One of the articles mentions Lightning Network with instant transactions and low fees, which to me looks very interesting.