I'm sorry to tell you this, the Swedish government may not mean to sound like they're begging, but they do, in a real pathetic way
To me it sounds more like whining, than begging, but I would agree with the fact that it does seem rather pathetic.
To answer your original question, as to why the Swedish government is asking for something they will never get; my analysis is that it's a desperate attempt to get themselves out of a tricky situation of painting themselves into a corner on the immigration issue. On the one hand the government has committed itself to helping all asylum seekers and is thus not willing to adopt more strict limitations than those they agreed to recently with the opposition (bar the Left and Sweden Democrats) but on the other hand they're also out of money to pay for more immigration and are not willing to make any substantial cuts to other areas to finance the increased costs. The idea that they can appeal (or shame) other EU countries into doing more is their last hope of get out of that predicament.
It's pretty futile, but they have to signal the Swedish people that they are doing something at least.
