~ What I'm wondering is what would happen if bitcoin's price reached a level that was so insane that 1 satoshi was something like $5 or even higher. Would that not screw up the entire bitcoin system? There would be no way to send small amounts of bitcoin or very exact amounts, much less pay a fee to the miners. Am I missing something in that hypothetical case other than the fact that 1 satoshi will probably never be worth that much?
Let's assume 1 satoshi is $5. Since 1 Bitcoin is equal to 100 million satoshis, it makes 1 BTC worth $500 million. When finding a block miners receive not only transaction fees from all the txs included in the block, but also a block reward that is 12.5 BTC currently.
12.5 x 500 million = $6.25 billion
If the block reward was so high, miners would start including transactions with zero fee without any problem, because only to receive the block reward would be more than enough for them.
And even after 2020 halving, when the block reward will be reduced to 6.25 BTC, even then, and I would say, many years after that, the block reward would be the main source of miners' income in the case of very high price of Bitcoin, not the transaction fees.