But a 51% attack has no reward. And if a 51% attack happens, Bitcoin keeps on working
51% attacks can totally be profitable.
It could just be normal mining where they produce empty blocks, or censor transactions of specific entities. They can get block rewards while still causing enough chaos to persuade others to switch to their side.
If a 51% attacker produces blocks normally, but reorgs 25% of its competitor's blocks, eventually its competitors will give up and stop mining. With fewer competitors, its work becomes easier and cheaper. Even more profit for them.
If the 51% attacker uses withholding attacks and selfish mining strategies, they could increase their profit even more. It's extremely profitable for 51% attackers.
-----------
No imagine that Bitcoin's security budget drops to the point where over 50% of miners are no longer profitable, and they threaten to fork and continually attack Bitcoin until Bitcoin adds tail emissions. If a blockchain war breaks out, those 50%+ miners are going to win every time. Other miners would be forced to join them or else their blocks would get reorged.
If a CEX doesn't play friendly with the miners, the miners would censor their transactions. If the CEXs and nodes jump to a new blockchain, the attackers can jump too just to harass them. If the CEXs switch mining algorithms while still staying on PoW, they'd be starting from scratch.
1. 51% attacker need to have lots of initial funds to obtain ASIC and pay opertional cost, while waiting for any CEX and miner join them.
2. CEX would hesitate to join with the attacker due to pressure from government either because their treasury contain Bitcoin or pressured by investor who buy Bitcoin using CEX, ETF or something similar.
3. Those who hate Bitcoin will take this opportunity to share news about Bitcoin isn't secure or decentralized, which will impact Bitcoin price negatively.