At least in the case of New York they still tax non-residents on income earned from New York. (I realize it may be less for non-residents than residents). It seems strange that I am legally obligated to pay taxes to a State but have no vote in the choosing representatives who levy those taxes.
That's a good point. That's a thing in California too. There's a 540NR for reporting non-resident income earned in California. I guess it never seemed 'unfair' to me because when I was a non-resident I was a student who spent most of my time in CA, and that's where I worked, so it seemed logical.
In some more complicated situations where you technically earn money in the state even though you don't have a home there, I could see how it would feel unfair. (I can't think of such a situation off the top of my head, but I'm sure they exist.. actually the athlete example might be a good one).
Yes, that's true. Most people who work in a state use some of that state's services (e.g., public transit, emergency services, etc.) and hopefully the state they do reside in gives some kind of credit for those payments.