The irony is that entering into a debate with them about how much it cost, likely cost far more than £585 in their time spent finding out. Reminds me of the whole "MP's expenses 'scandal'" - the inquiry cost more than was paid out originally in expenses. £585 is nothing in that sort of context.
As to the MPs' expenses stuff, I don't know the figures of how much the inquiry cost, but assuming you're right that it cost more, it doesn't mean they shouldn't have done it.
For one reason, ethics - should police ignore crimes when it appears that the damage caused by the criminal is less than it would cost the police force to pursue it?
For another, the future - If you cut off the problem then it doesn't keep costing money year after year, which would add up to costing more than the inquiry did.