Assuming you are employing hyperbole I'll skip over the idea of it costing more than £585 in their time to find out.
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.
I'm not in the least... It probably took them an hour to find out, reply to the emails etc. They probably had to ask others etc. Their salary, electricity, office overhead etc. I'd expect it came to a fair bit more than £585 to deal with the request for information.
The MP expenses thing was always ridiculous. So an MPs husband mistakenly put in an expense claim for £10 adult movie. Sure it sells papers, but £10 is nothing. We spend more on paper cups in a single room of the NHS.
The rules were ridiculously open to interpretation - second homes etc. Couple that with the fact that MPs get paid next to nothing, and it's no wonder they try to claim expenses for everything.
The answer is to pay MPs more - the going rate for if they're in the business world. If you don't want corruption or taking liberties, you must start by paying a fair wage.
I agree that MPs are relatively underpaid [1] and mistaken adult movie claims are a cause for embarrassment rather than the source of the national debt.
But I don't think it's ridiculous to prosecute MPs who defraud the public by claiming "homes" belonging to other people that they've never even stayed in; even though the prosecution costs far more than the actual offence. Lines have to be drawn. It's expensive to prosecute people for shoplifting too.
[1]underpaid enough to be justifiably anal about claiming expenses; not so underpaid that doubling their income by home flipping is the only way they can feed their families
Can also dissuade good people from going into politics if their every expense will be scrutinize nit-picked etc.
Why put up with all the BS and low pay of politics when you can go work for a big company and run up massive expense accounts for lap dancing clubs or whatever else you feel like?
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.