stake system seem more sustainable in years to come. so why is better to pay to mine coins and use power?
Take a read of this:
https://bitcoin.org/bitcoin.pdf
You will see that proof of work means that people paying electricity to carry out work are what secures the network. Proof of Stake means nothing.
I agree it some security but there no true network security.
bitcoin even can get 51% attack.
It seems to me coins that stake and use no power can survive in future without spending power.
Proof of work was partly invented to stop email spam.
If you use PoS, you create spam. A few people able to create many staking wallets. That is partly why PoS = proof of shit (jack shit, i.e. nothing).