am I a big jerk?

At my new library we have lots of computers for the public to use.
In fact computers are probably one of the main draws for the public to the library these days.
However, most of the people in this neighbourhood refuse to get cards.
This angers me.
First it angers me that they have been tolerated and placated and given "one time uses" for the computers. This is ridiculous, especially since the policy is that if you live in the city of Toronto and wish to use the library you MUST get a library card. We have made getting a library card as easy as it legally can be. (you just have to have a piece of ID, that is all you need)
However the public here have a thing about anonymity. They don't want us to know who they are. At all. So they will refuse, argue with me, get beligerant, you name it - all in the sake of avoiding getting a library card.
To me this is just plain nonsense.
And well I am determined to make this branch a nicer place, since I was told to do that when I arrived. How is one of my approaches to this? Make them get library cards, that way we know who they are and can then take legal action if it is necessary.
So now I have the unique issue that most of these people will not get library cards. They will argue with me, I will refuse them computer use (unless it is for a good reason), and they leave. So in part the branch is quieter, but alas, we are not getting people to get library cards.
See, the other reason I want people to get library cards is a selfish reason. It is because statistics are how the library board decides wether or not we are succeding as an institution. The more people who get library cards, the better are statistics, the more funding we are guaranteed from the city. I even use this logic as one of the reason's why people should get a library card. They dont' care.
To be honest, I think that libraries could become obselete in the future. There are libraries closing in the United Kingdom, due to lack of use. I think that could very much happen here. So not only would I be out of a job, but also there would be less access to information or information portals. And I think that is very sad for everyone.
So it angers me that this population is so selfish, that there only concern is to check their email or facebook and then leave. That sustaining something positive and worthwhile is not important to them, now I know that this cause may not be everyone's cause - but then why do these people want to use the library if they don't want to support it and ensure that they can come here 20 or 30 years from now and have it still be here?
As I refuse these people internet access since they refuse to get a library card I always think to myself - "am I being a big jerk?", should I just let these people have the one time use, let them do whatever? And then I realize - that giving them the one time use changes nothing, except making my job harder. At least if they leave the library I don't have to deal with their nonsense, and maybe eventually they will get a library card.