marksawatsky
It's unfortunate that this is your first posting of a thread as I suspect it may not elicit as much discussion as befits your effort. That's because we had similar a discussion many moons ago when the points system was revised to the current format, and every now and again we chew it over when Bernie comes up with something like his suggestion for a medals system .
I originally wrote a comment that was very negative and perhaps a tad flippant so I deleted my initial thoughts as I fear my style of humour would have gone down like a sack of spuds if you're not yet familiar with my material.
So, taking your OP seriously - i.e. treating it with respect and ditching my usual flippancy - I'll share this much and I apologise for the fact that it isn't positive and I hope at least that you're not offended. I say this because you may well have been really pissed off about the original version

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So, I actually think the points system is okay although there is possibly too much of a gap between points for the win and second place and that the stupid double points at the last race should be ditched.
Awarding points for qualifying or fastest laps I feel would only increase the points gap between the guys in the faster, most dominant cars and the also rans. Yes, we might get balls out one lap wonders who can put in a fast lap in qualy' and fastest lap in the race scoring points they would otherwise not get, but a drivers' overall performance in the race is what counts. Outright speed is not the sum of the drivers ability. Can the bloke overtake people, avoid crashing, play fair, keep his head, look after the car and stay out of trouble yet finish higher than he starts, etc. etc. Loading points for overtakes and leading the race I would suggest again favours the dominant team and driver combo so I don't believe the extra points would be helpful or meaningful.
Having said all that, if points were to be awarded for every classified finisher and the prize fund was based on the points as a multiplier then there might be a purpose. It would require a significantly bigger share of the F1 income pot that currently lines the pockets of CVC shareholders to be redistributed to make the new system worthwhile. The upside would be more money for the less funded teams. The downside is that some sort of "success deduction" would be needed to apply to the big spenders who generally have the best packages. Otherwise they would get even more income and even fatter budgets totally negating the system. The thing is that proposal would be kicked out of the ball park quicker than a gnats blink due to the current power relationships in the structure of F1. The pecking order of a handful of "major teams" (no prizes for guessing who they are) wouldn't back it for selfish reasons and the sports owners (CVC shareholders) ain't going to share their luvverly lucre!
Of course, anything is possible if we get another political storm strong enough to prompt a breakaway series! Sorry, that's as positive as I can get on this one.
Finally,
marksawatsky , don't be dispirited if we can't do your first thread justice. Welcome aboard Clip and keep on posting.
Fenders.