SE is famous for implementing overly simplified systems though (imo).. I'm not saying that this tally system cant be a problem - but that it can also not be.
If people are asking for competition then a system of tallying and contribution is far more competitive and a better form then the milisecond it takes to claim the monster.
To design a system that semi-intelligently tallys people would take a while though, because you would have to create dynamic calculations and not just "1 damage = 1 point".
Otherwise if you introduce a system where everyone can contribute but no pressure to do well then there will be a bunch of free loaders. Designing bosses to occasional smash free loaders could be another funny mechanic.. lol
Edit: AttackKat apparently said Yoshida talked about a similar system for claims in the first place.. So maybe I dont even need to mention this if Yoshida is already thinking about this stuff lol
Perhaps a part of the point system can be claiming (for lesser nms and monsters) - if you get the first hit / claim then you get a bonus amount to you or your party. That way its less likely a group of people come by and fully steal your monster (like if you were a red mage trying to solo a monster and a group of black mages come in and penta nuke him - you'd still enough points to matter for some loot). I think for the big ass NMs though that claiming really shouldnt be a part of the contribution ranking - since the fight is so long your .1 second is like .0000000000001% of the actual fight.
Furthermore you could make the point system relatively competition free - just use it to make sure players actively took part in the battle and then loot rewards are independent of whatever points earned. You could also use the points for achievements. Like a "hamlet" of HNMS (score tally board at the end) "knock off tail +100 points, x y z and earn 100000 points on nidhog to get this special achievement title and item". Can make the points a total rather then all at once event so return visits to HNMs encouraged.