As a layman, I've always understood that there is a general consensus amongst economists that "immigration is economically beneficial" to rich Western countries (like Britain) who have aging populations because the influx of young economically active workers contributes to the economy (and tax coffers) and thereby supports the old economically inactive population.
But this seems quite obviously short-sighted. Those immigrants will themselves grow old—and assuming that they remain in their new host countries, they will add to the economic burden of the elderly populations for future generations.
Is such immigration therefore not just kicking today's problems into the future, where it will have compounded and be exponentially worse?