I'm not entirely sure if you've used Bitcoin before, but the transaction fee is basically a way to pay a miner to put your transaction into the block they're mining. A higher fee gives miners a higher incentive to add your transaction. But it's generally just a flat value, not tied to the amount being transferred in the transaction - don't think of it as a tip, think of it as paying the miners to take your transaction. Depending on the digital currency you're using, adding too small of a fee may mean your transaction is never added to a block and thus never actually happens.

For Bitcoin in particular I haven't been paying too much attention recently but I do know transaction fees have been getting much higher the past few years, like 5 to 10 dollars or so (Which means you have to pay 5 to 10 dollars to transfer any amount of Bitcoin from one address to another).

I have not used it before. I just assumed that - whether a percentage or a flat fee - the amount would be... deterministic at least? That the entity being paid the fee would at least state their price somehow, instead of the user having to just, like, guess what their tribute should be and hope it's accepted. What you describe sounds incredibly bizarre to me.

Well keep in mind, your transaction basically just floats out in the void until a miner adds it to their block, so you have no idea who's actually going to add it (if anybody does) because due to how Bitcoin works you have no idea who's going to mine the next block(s). It's also basically another market to a degree - It's not really about how much a miner wants as much as how many transactions there are with a particular fee. The blockchain only supports so many transactions per block, so if you send a transaction with no fee and there's enough transactions with fees to fill every block (like with Bitcoin), your transaction will likely never get picked up because there's no reason for a miner to take it.

That said, I agree I'm not a huge fan of a system, but it makes some sense from the standpoint of how Bitcoin works - miners are paid for their work via new bitcoins created as part of their block. But, Bitcoin itself is designed to be deflationary and eventually the number of new bitcoins per block will go to zero, leaving the fees as the only way miners get paid. And the fees thus aren't deterministic as a way of allowing the amount miners are paid to vary over time.

Still, I don't think it's quite as bad as you're thinking - it's not really hard to figure out what an acceptable fee value is with a quick google, and it doesn't really change that much day to day.

The article states:

"Ethereum users can dictate the terms of their transactions, setting both the amount of ETH they want to send and the amount of fees they are willing to pay. The higher the fee, the thinking goes, the more likely their transaction will be included on the next block — i.e. it will go through more quickly."