Citizenship gives rights and creates obligations. That relationship is worth discussing without assuming that making citizenship more widely available must either strengthen a country or destroy its meaning.
Rome offers an interesting example, though not a ready-made answer for modern Britain. In AD 212, Caracalla extended citizenship to almost all free inhabitants of the empire. A status previously distributed much more selectively became far more general.
A motive isn't the whole consequence
Cassius Dio linked the measure to the emperor's interest in revenue, including taxes associated with citizenship. That is an important contemporary interpretation. It isn't a complete explanation of every motive or a demonstration that the reform failed in every other respect.
It would be a large leap from the edict to claiming that wider citizenship destroyed Roman loyalty. An empire's history can't be reduced to that one change, and our disagreement about modern welfare isn't evidence of what Romans felt.
What the example does show is that a change in membership can also change a state's relationship with the people it governs. The rights and duties attached to the status matter alongside who receives it.
What does membership ask of us?
A modern country can expand citizenship and still expect commitment from its citizens. Membership doesn't need to be scarce to be meaningful. It needs some shared understanding of what belonging involves.
I think people are entitled to ask what citizens owe one another, how contributions and entitlements relate, and what someone joining the country is expected to accept. Those questions needn't imply that people in need have no claim to help, or that financial contribution is the only kind that counts.
The argument becomes less useful when openness is treated as the absence of obligations, or obligations as proof of hostility to newcomers. We can welcome people into a country while being clear that they are joining a community with responsibilities. Roman history is a reason to examine that relationship, rather than a shortcut around the argument.