All the work in Bitcoin mining is going toward making it harder for someone to rewrite the history of Bitcoin transactions (which would allow them to take back

All the work in Bitcoin mining is going toward making it harder for someone to rewrite the history of Bitcoin transactions (which would allow them to take back sent Bitcoin). More miners means it's harder for any attacker to rewrite the transaction history. The protocol incentivizes people to mine (and simultaneously solves the problem of deciding who to distribute newly-minted Bitcoin to) by distributing the fixed amount of newly-minted Bitcoins between the miners every ten minutes. Bitcoin's security relies on the true blockchain having more Proof of Work in it than any attacker could create. A Proof of Work value is a proof that you had a computer spend about a certain amount of processing time tied to a specific input value. Someone with one computer can't produce Proof of Works as fast as someone with multiple comparable computers. Someone trying to take-back a Bitcoin transaction and create an alternate blockchain with their transaction removed can't create Proof of Works as fast all of the world's Bitcoin miners working together (unless they have a secret god-tier supercomputer, or somehow convinced most of the world's existing Bitcoin miners to work for them instead).