Securing traditional monetary systems also had to deal with the fact that we cannot trust each other (enough, in aggregate), and I think that's where most of the expense goes.
The point is, Bitcoin can end up saving a lot of energy, by replacing traditional banking transactions, while everyone seems to be seeing it as "wasting" energy. Everyone sees the glass half-empty. Bitcoin only needs to be mined for another few decades, and then it won't need to be mined anymore.
Bitcoin will still need to be mined - the whole 'trust' system is built on it, just the block reward will be zero. Miners will then profit only from transaction fees, so either the fees will go up or difficulty will go down to adjust for smaller income from mining.
The actual purpose of mining is to extend the blockchain. It just currently has the incentive-producing side-effect of creating bitcoins. In the end, mining will be funded through transaction fees.
Others have addressed a point on which you're mistaken, but it could still be that bitcoin proves cheaper.
My concern about bitcoin winding up more expensive is that it's a bit of a red queen's race. Unlike most applications of encryption, attackers and defenders are on even footing (except, like in most human spheres, in that defenders hopefully outnumber any coordinated group of attackers). This means that whatever latest best tech we have for efficiently turning power into hashes, we've still got to burn about the same amount of power to keep things secure (and continually update to the next newest tech). In other spheres, technological process makes doing the same work cheaper - but in bitcoin it stays the same; you've got to run as fast as you can just to stay in the same place.
