I don't know if this is the truth but I remember reading that the parts were pretty much there for Nick and Paul to play on the first album as the band were still finding their feet. But after that album they became more of a 'proper' band. Also, Mark Hart has mentioned in the past how Nick sometimes took a while to find his part in the studio but it was usually pretty special once he did.
The fact the majority of songs are credited solely to N. Finn only tells us that Neil wrote the melody/words/chords (essentially the song ) but not necessarily the bass parts, drums, keyboards, etc. As the main songwriter you would only tend to give someone else a songwriting credit if they provided a decent part of the lyrics or melody or changed the structure or style of the song in a major way (ie Mitchell Froom's credit on "Something So Strong").