Mining is done on ASICs while verifying transactions and building blocks is done on CPUs so they don't really compete. If a transaction includes fees, miners have essentially no reason not to mine it.
CPUs mining that transaction into the blockchain will be even slower than ASICs (100M hashes/sec vs 1G h/sec). Moreover, a LOT of miners have to do this work and it doesn't clear until the last one does the work.
This is slow. It's not cheap simply because it's done on cheaper HW.
They said CPUs are NOT used to mine and it's true. All (successfull) mining is done on ASICs.
Also, not every miner must do this work. The transaction "clears" as soon as ONE miner solves the puzzle then includes the transaction in that block. The other miners only have to verify it which takes a only a tiny fraction of the amount of work needed to solve the puzzle.
It is slow but it's almost always faster than international (as well as domestic for some of us) wire transfers. Also, there are a lot of people working to make it faster.
It's currently a pretty crap currency for most people in the world but it has potential to completely change the world. This potential is reflected in the market cap.