Why do we need another way do give points? What is wrong with the one we have?
The ultimate purpose of the point system is to be able to see who is 'the best' driver and car along the whole year, the whole season, teh whole round of races. But, as soon as you establish rules, as in any aspect of real life, the drivers (and anyone) will try to use them in their own favour. What does this mean? This means that drivers can not always try to win the race but just 'stay alive' for the next where situation can be more favourable - specially now when races have efects in others in terms of mortor and gearboxes -.
There have been several scoring systems along teh more than 50 years of Formula One history, probably considering all possible variartions: giving points to teh fast lap of teh race, discounting
Some people (me, for instance) think that teh actual point system does not award winning a Grad Prix enough and, in some situations, drivers will then prefer to wait for a better situation in a coming Gran Prix than risk overtaking and lose the current amount of points. I do vbelieve the win must be worth enough to fight for it till the end of the race.