Bitcoiners hold that immunity to central control is so overwhelmingly important that it’s completely worth all that electricity wasted on mining. And the maths is unbreakable!
In practice, mining naturally recentralises due to economies of scale, so a few large mining pools now control transaction processing – and even though the cryptography is mathematically robust, the rest of the system is approximate, with attacks being a matter of how much economic power you can bring to bear. Pools with a large percentage of the mining power can attack the system in various ways, and have been caught doing so in the past. (See Chapter 5: How Bitcoin mining centralised.)
And that’s before even considering bad user security, or exchanges written in dodgy PHP. Bitcoin’s cryptography is solid, but it’s a bit like putting a six inch thick steel vault door in a cardboard frame.