Because they are underfunded, Bezos seems to be addressing that.
>>kind of my point, no?
No, the provided example seems to be counter to your point.
If those with the means paid a fair price for the library resources they are sharing, a library could be open for many more, have better resources AND cost the taxpayer less.
Libraries weren't always free. Like the one Ben Franklin helped establish. These didn't cost the taxpayer anything. And if you wanted to help someone without the means, you would just pay for their membership.
Making something free for some, but not others could stir up resentment ("why should I pay for your use of the library?"), which would make it easier to cut funding in the future. This could lead to a spiral of increasing fees (or decreased service) -> smaller constituency -> less funding.
I'm also not sure that the marginal user costs a library very much. I doubt that a library with twice as many potential patrons needs twice as many books or two times the staff, for example.
A month's worth of food costs a lot more than using a book for a month.
In the US, Republicans have been talking about "welfare queens" and people buying lobsters with food stamps for literally decades. This strategy has apparently worked for them, even though benefit fraud is supposedly quite rare.
On the flip side, it's virtually impossible to cut Social Security and Medicare in the US, in part because the programs are not means-tested and everyone hopes to get something back from them.