I have an interest in the Arabic parts but I must admit that apart from the Part of Fortune, I only tend to look at them when doing a horary. Though from my limited knowledge, I think that their traditional use was in horary or event charts.
Arabic parts are a type of mid point, so they seem as valid to me as any other use of midpoints - their position being dependent on usaully two planets and the Ascendant (though this is by no means exclusive).
I'm not quite sure what Dave means when he says they don't move. It's true that there are no ephemerides charting the movement of Arabic parts but as the planets move, then so will the parts which depend on those planets, though they only 'point' to a degree of the Zodiac that degree changes as the planets move and as the Earth rotates. An Astrological chart is nothing more than a snapshot in time but if you took two people born say an hour a part you would find that their Parts of Fortune were different - indeed the Part of Fortune 'moves' as fast as the Ascendant.
Dave is quite right in suggesting that the Parts give the chance to extend the range of Astrology, with a limited number of planets, although I've seen 'modern' parts which include Uranus and outwards and no doubt someone, somewhere has invented one which uses Asteroids.
The modern approach is to search out asteroids, chiron type objects, Kuyper belt type objects and indeed hypothetical planets in order to extend Astrology. All of which also allow Astrologers to raise their fees!
There is an argument for saying that the extension using parts is more reliable because at least we have a reasonable understanding of the Seven visible planets. That being said the 11th Century Astrologer Al Biruni complained about the rapid growth in the number of parts and questioned their validity - just like me and the Asteroids - plus ca change.....