The analogy holds precisely for the reason that San Jose does not consider itself beleaguered by the influx of immigrants who want to live there. The fact that you could entertain thought experiments in which the net consequences of immigration are negative (e.g., a giant flashmob of 50 million people immigrates simultaneously) does not suffice to show that San Jose's hospitals and roads are overwhelmed in the actual world.

In the actual world, San Jose is not in fact appealing to the federal government for assistance; it is reaping the benefits that attend a growing metropolitan population and tax base. On average, San Joseans are better off when more people become San Joseans, for all the same reasons that New York is a more desirable place to live (as measured by the demand for housing) than Wichita.

I've never claimed that there are no states who do not take their citizens' interests into account. I claimed that states often take little or no consideration of the interests of non-citizens. In absolute terms, for example, malaria is a much more pressing human affair than corn subsidies. But corn subsidies primarily affect people within the US whereas malaria primarily affects people outside the US, so corn subsidies dominate malaria in contest for the attention of the US government.