The miners get paid less and less as time goes on.
With the ledger also growing bigger and bigger, wouldn't the cost of mining start to exceed the profitability of mining? If no one would mine bitcoins anymore, wouldn't it shut the whole system down?


Thanks to moore's law, performance of mining hardware improves over time. While power consumption decreases. The value of bitcoin also increases.
These factors coupled together can translate to greater net dollar rewards, even if
BTC rewards halve every 3 years.
Everything miners are able to earn past their break even point is free money. Long term electricity consumption and hash rate difficulty become the main factors.