There is a disadvantage if it turns out that these people make on average a negative contribution to the economy (i.e. if the aid they need and damage they cause via crimes is higher than the surplus created by them aiding others, and producing useful labor, good and services), which would mean that they make the people already there worse off and worser off the more of them are allowed to enter.

I'm not sure whether they are a positive or negative contribution, and this also depends on how good the accepting state is at integration and education.

Or they could bring them back to their port of departure on the South of the Mediterranean, so they can try to enter legally. (or better not at all.)

People without work permits are either dependent on government support or contribute to worsening working conditions for everyone by working illegally. More resources have to be spent to make them productive.

In the best case, taking in random people off the boats is still worse than a capability based immigration policy that encourages people with qualification to immigrate safely.