It has something to do about terminal design.
Equipements, handlings and airport services has to operate at ground level. That's where departures and arrivals at an upper level came from. There is not always the necessary room to lay everything at ground level. Though, thousand of smaller airports are not multilevel, mainly because they don't have that much passengers and cargo movements to justify the amount of investment to do for such extensions.
But why, when cost is not an issue, departures are usually above arrivals ?
Cost is always an issue. Pragmatic and practical reasons :
Elevators, speedwalks, escalators... works with electricity and must be maintained. The more you add those in the design, the more it costs. You can avoid them when you were able, by default, to bring most things at an higher level, and let them move with the help of gravity, or at least, reduce energy consumption by limiting the cases where something or someone has to go at an upper level. This doesn't explain why departures are usually above arrivals, but is the start of some explanations below...
as I said, luggages can be moved with the help of gravity. Let's assume departures are at ground level and arrival upstairs. Passengers's luggages go straight through checkings upon departure, then are loaded in the aircraft. Arriving luggages are unloaded from the plane, then goes upstair (move up). If it was the other way around, departing passengers's luggages goes downstair (move down). At this stage, the only difference is the move up/move down. When it comes about cost, it's better to move down only.
But, upon departure, you not only have to check-in. There are control checks, and in case of international flights, extra checks. That is available space concern. Plus, you add boarding area with benches/chairs, duty free, lounges, and other goodies that consumes space. Obviously, you ought to have a lot of available space for your terminal to have both departure flow and equipement services at the same level. That's why, on some terminals, arrivals are on the same level as those equipement services as they require less formalities than departures, and can be designed to fit on the same level as services. => departures on the upper level.
Parking lots. By design, it cost less to set parking lots at ground level. It's much more expensive to place them underground. While raising them above ground can be much more or less expensive than underground ones depending on the circumstances, it's usually assumed it would cost much more. Most frequent practice is to bring departing passengers in front of the checkings (few steps to do) then park the car. Reciprocally, arriving passengers has to bring their luggage on their own to the parking lot, as it's uncommon to let hundreds of car peacefully wait in front of arrivals. If most parkings lots are at ground level or underground because of design cost, it's more practical to align arrivals with parking lots, or at least, narrow the difference in levels, both reducing elevators or alike usage/congestion, and amount of effort required from the passengers to reach their vehicle. (also note that on some airports, you can't bring luggage trolleys outside the terminal, meaning, you have to pull your 40lbs bag all the way to the car)
It's better to wait in a roomy area than a narrow one. Think of the difference between waiting for boarding upon departure, and waiting for your luggage upon arrival. Even if it's usually wrong, it's assumed that you spend more time waiting for boarding upon departure, than waiting for your luggage upon arrival :P Well; in fact, to help you stay in a good mood and be open to spend some $$, departure areas are usually rooooooomy and beautiful ! You can only take advantage of that on the uppermost floor. People don't buy that much things upon arrival. They just want to have a rest, or get on time at their meeting or connection.
On a passenger's point of view, what matters is the distance one has to walk with that 40 lbs bag (even without) than anything else, no matter it's departure or arrival. Stairs are poor designs and not practical for trolleys. Elevators are known to be prone for traffic jams. The departure above arrivals is the design that best suits this requirement, and doesn't cost too much.