What if they don't have papers? What if their country hasn't registered them? What if they lie about their name and birthdate, so their home country cannot identify them? What if the home country doesn't want them back? People don't go to UAE because life will be worse there.
Your encouragement argument has no base in reality. You live your well informed western perspective. These people have no idea where they are going, what life will be like here in the EU (terrible for many). They take the risk because they have nothing to lose: famine, natural disasters, never ending wars, dictators. They don't do this because they are encouraged somehow, except that they can't stay at home anymore. That is the "encouragement" indeed.
The journey is not "hard". It's insufferably hard. Everything you have will be stolen. You may be kidnapped to do slave labour. You may get raped, killed, or see your mates get killed in front of you. And that is before you step in a small boat with tens of people to cross a sea with no navigation, not enough food or water.
When you enter Italy and see your refugee status rejected, you enter the human void of being "illegal", undocumented. You live by the day, no future lies ahead of you.
If you get accepted, you may have lost seven years living in some kind of open prison, no language lessons, nothing to do all day.
Talk about "encouragement", but this doesn't stop people either. So why would this encouragement argument only work one way? Because the discouragement measures do not work at all.