51% is also not very viable for proof of work either.
What 51% gets you is that 51% of the time, you get to choose which transactions go into the blockchain. This is mostly only useful if you want to prevent someone else's transactions from getting in, or for complicated scams where you want one person's transactions to get in before another person's. 49% of the time, those transactions will still get in, so 51% actually doesn't buy you a lot. At best you cause a short term chain split and people will wait longer before the chain stabilizes.
What 51% gets you is that 51% of the time, you get to choose which transactions go into the blockchain. This is mostly only useful if you want to prevent someone else's transactions from getting in, or for complicated scams where you want one person's transactions to get in before another person's. 49% of the time, those transactions will still get in, so 51% actually doesn't buy you a lot. At best you cause a short term chain split and people will wait longer before the chain stabilizes.