I can speak to the past 25 years or so for distributed stuff. The number sent out in general are the same. Recently studios are starting to not send out rated finals if the poster is unchanged art wise from what was sent out. Not always, but it has been happening more and more of late.
Advertising budget will often drive whether a new style is put out for the final or not. This also varies greatly from studio to studio. Lionsgate is by far the best marketer using paper these days. They still print up a bunch of different posters for many of their films. Paramount, WB, and Universal are getting pretty lazy, and will just print up the same poster with credits often unless it is a big budget summer film. Sony is kind of split down the middle. A lot of their finals these days though, have just a ratings box and no credits block. Disney is pretty good about doing an advance and final for anything they expect to do 100Mil or better, same with Fox. Indies, you normally will get 1 poster, unless distribution of the title changes at some point, then you will get another rebadged, and often different art.
Desire.. up to each buyer, nice looking posters sell crappy art doesnt! Some only buy advances,some only buy rated/credit block finals. Everyone has their own preference.