Here in the UK, if a government department has pissed me off, I make lots of freedom of information requests to cause them hassle, and quite often data protection ones too. What is the situation in the united states for things like this?
We do have FOIA requests. I’m not sure what you mean by data privacy requests. I do know Europe and the UK tend to have much stricter data privacy laws than the US.
I can’t say I’m thrilled with your approach. The government employees you may annoy no doubt get paid regardless, while raising taxes for everyone to handle your pointless requests.
I’d recommend reading the book *Equality and Efficiency * by Okun, which fought some of my ignorance about government and may do so for you as well.
This reminds me of the suggestion made in the 1960s by the anti-Government, anti-business crowd that we all overpay our public utiltity bills by one or two cents, thereby causing the agency or company involved a lot of extra work recording the extra penny or two. It was a stupid, pointless idea then, and your idea isn’t any better.
And if you annoy them too much they can get you labelled as Vexatious, which means that they can ignore you.
Do you do this often? How many times have you done this? What’s “lots” in your case? And, why do you do it if merely to “cause them hassle?”
Of course, what the OP neglects to say is that often there is an administrative charge for Data Protection etc requests. This can be up to£10. So as well as asking how many times they have done it we should also ask how much they have wasted doing it. 
It’s a stupid idea. People have DPA and FOI requests as part of their job duties. It’s no skin off their nose to do them because that is their job. Nobody gets annoyed.
I wouldn’t go that far, at least speaking from a U.S. perspective. While there may be people administratively responsible for FOIA requests, actually responding to the request often requires a subject matter expert to take time away from his or her priorities to respond. When annual appraisal time comes around, that person will need to account for getting their projects done according to plan, with or without FOIA requests.
Does this really make you feel good?