The meta analysis you link doesn't seem to quite agree with the way you're framing it. Quoting some of the relevant paragraphs:
> The likelihood and magnitude of adverse labor market effects for natives from immigration
are substantially weaker than often perceived. Within the large empirical literature looking
at the effects of immigration on native employment and wages, most studies find only minor
displacement effects even after very large immigrant flows. On the other hand, some more
recent studies have found larger effects, and many studies note that the negative effects are
concentrated on certain parts of the native population. The parts of the population most
typically affected are the less-educated natives or the earlier immigrant cohorts -- that is, those
who are the closest substitutes to the new immigrant flow currently experienced by Europe.
> Immigration is often viewed as a large fiscal burden for European public finances or as a
possible saviour if correctly harnessed. This has been palpable in the recent political atmospheres
of France, Italy, and Germany, for instance. Most empirical studies, however, estimate the fiscal impacts of immigration to be very small. There certainly exist large differences across migrant
groups in the costs and benefits they cause for a host country; the net impact depends heavily
on the migrants age, education, and duration of stay. On average, immigrants appear to have
a minor positive net fiscal effect for host countries. Of course, these benefits are not uniformly
distributed across the native population and sectors of the economy.
The gist being that overall the adverse effects immigration has on the market is much smaller than people perceive, that those most affected are either the prior generation of immigrants or those with less education and that the negative fiscal impacts are negligible at best, with immigrants generally contributing in a positive way.