The procedure you're proposing collapses into approval voting immediately.

Nobody has any reason to vote anything else than 10 (possibly minus epsilon) or 0 (possibly plus epsilon). If you like A slightly more than B, and estimate A will get 81 points, while B will get 90 points, the optimal behaviour is to vote 10 for A (and everything better than A), and 0 for B (and everything worse than B), any other vote is strictly worse for you. There is no scenario under which voting anything else than 0 and 10 is better than extreme votes.

Approval voting is prone to tactical voting (this should added to requirements, Arrow's Theorem talks about preferences, as it assumes voting is uniquely determined by them) - you never need to order candidates in a way that reverses your preferences, but approval threshold depends on what you think others will vote like. If you think A > B > C, and think C is leading, you vote 10,10,0. If you think B is leading, you vote 10,0,0. It also fails at determinism.

If we give people predefined allowance of points (like n alternatives need scores 1 to n, or get n points for arbitrary distribution) it fails independence immediately, and is prone to preference reversal in tactical voting, which is even worse (if A > B > C, and C is leading, but B has some chances, you vote 0, 10, 0, with A < B).