>What it will do, is actually drive up the cost of all business, and worsen employment simultaneously.

That's the point of raising interest rates. It's demand destruction. If raising interest rates didn't raise the cost of doing business, it wouldn't work.

>You can typically see a rise in prices (inflation) following a rate hike. Even when it's needed to combat regular elastic demand side inflation, it takes time to have a positive effect.

Are you sure it's not just reverse causation? eg. inflation has gotten so out of hand that bankers are raising interest rates to counteract it? After all, inflation isn't a random walk. If it's bad one month, it's likely to get worse the next, especially when central banks haven't raised interest rates yet.