Isn't VAT wrong?

I've often wondered why business-to-business transactions have to pass cash up the chain and then reclaim it from their VAT payments.

Wouldn't it be a lot easier if business-to-business transactions didn't require this money to slop around. Sure, obligate the supplier to validate that their customer is a bona-fide business (and charge VAT if necessary), but just stop the default VAT charges.

With no money floating around the system they'd be no VAT fraud. Also there would be less temptation for ailing businesses to 'dip into' the VAT account.

Or is this too simplistic?