Open Borders: The Science and Ethics of Immigration provides arguments that, overall, the benefits of open borders outweigh the costs.

Citizens are asked to contribute to building up the country via taxes and other means now and over their family's history in that country. This could be seen to buy them "equity" in the resulting labor market.

The country you are born into is just a matter of luck. Why should this entitle you anything?

I think there's an argument to make about citizens/residents having special access to social benefits (or at least it being tied to some period of residency — the "equity" @andrew mentions), but I can't see much if any benefit of restricting labour, except with the asterisk that I think it requires strong labour laws that enforce societally-agreed minimum standards (to mitigate the effect of poorer newcomers being willing to work for less and employers therefore being incentivized to hire cheap, migrant labour).