The main reason is that people generally want to leave the airport immediately when they arrive. There is no point in making the arrival side nice since no one is supposed to nor wants to linger or wait there.
The departure side has the passengers who are waiting for their flights. In cases of stopovers, transit flights, and due to security checks, this might be quite a few hours of waiting. Therefore there must be waiting areas and, in modern times, shopping areas, waiting lounges, restaurants etc.
When you arrive at the airport, you are not really expected to stay there for much longer. You get your bags and you leave. In the departure sections, you might have to wait a few hours for a plane because you showed up early, the flight is delayed, or because you are transferring. It makes sense for this area to be nicer since people will more likely benefit from it.
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