Why would the people paying for the research not control what it can be spent on? Letting the people who spend the money decide is typically not a good system.
They do control what it's spent on. There are volumes of compliance about how you can spend the money. For example, can't use the funds on food, alcohol, paying rent, bribing people (yes, seriously, some idiot tried it and then they had to make a rule about it), you have to fly US carriers where possible, etc.
There are also reports you submit showing your progress and how you spent the money, to check that you are spending it on things you said you would.
This thread (not just the person I'm replying to) demonstrates a lot of misconceptions about why we have research funding, how it works, and what the results have been in practice. Please, everyone, don't rely on stereotypes of how you think research funding works.
typically
Pure science may not be a typical case, though, because the people who control the funds don't really have any idea whether the work they are funding is ultimately going to turn out productive or not. The work involved is far from routine and basically a jump into the unknown.
I get the risk of fraud and nepotism, but in some other situations (Bell Labs etc.), "choose very good people and let them improvise within certain limits of a budget" turned out to be very efficient. The devil is in the "choose very good people" detail.