What a wonderful world you live in. Do you genuinely believe it's that simple?
What do you think happens when 1 million people move from one country to another? They do not simply relocate, they are parked in camps (if you want current examples of that look at the Rohingya people, or Syrian refugees in Lebanon) until they can go back home, as you can guess the sanitary situation of these camp is more than precarious (cholera is a big threat for instance). With climate change, their will be no way back, and it's not going to be one million of people, but hundred millions.
What do you think would happen if a country, let say Italy for instance, had to park 10 million people in camps for years? Don't you think people in camps would eventually revolt violently to get out? What would Italians do then? Don't you think European countries would anticipate this outcome and just block refugees from entering, shooting the one trying to? Because it's already in the political agenda of most far-right parties here in Europe, and most of them are not that far from power (Salvini and Orban and just the first of a long series coming…). Due to the fight against illegal immigration, there already been thousands (around 17 000) of death in the Mediterranean see since 2014. And you can be sure it's not going to be better when all central Africa is uninhabitable …
And when people fleeing their countries are not accepted (as in “parked”) in neighboring countries, they just wander in the wild until everyone is dead. That happened for instance to people fleeing Rwanda to Congo.
Large scale population migration are incredibly difficult, and they almost always go wrong, and least a bit. Expecting 1 to 10% of the refugees dying isn't that pessimistic. From the figures discussed earlier, that mean between 2 and 150 million death. Which comes in the same ballpark as the biggest humanitarian disaster of the 20th century…