I, uh, don’t know, because I’m still building it. Convince me. Why do you think counting total points separate from events and awards would be useful? 
ok, let me try 
My thoughts is to use Achievement as the back office for the whole community. Things under this management can be(but not limited to):
1. Native Achievements Events– this is what we do currently;
2. Items from Custom Post Types– each type has its own item to track, and the points gained should not be mixed with other types.
For example–
Tracking student’s grade. A teacher can create an Achievement for a lecture and manually give grade to a student. This point can be under “Grade” category;
Tracking project completion. When a task is done, the project manager give points to the team member, this can be an honer, can also be a salary.
These 2 items have different value and must be evaluated by different means.
Another example, if you are not convinced yet–Tracking money transaction. Eventually, members need to cash out their points, but they can’t cash out their grade, right? 
You say you need two score categories. What happens when someone else comes along and says they need three?
no, I need more than 2 categories
)
you give us a hook with arguments, who ever want more category, he just hook up 
Or, as you said, just 2 categories, one for accumulate-able points, another for non-accumulate-able points.
@djpaul , How about this–
3 categories,
Events category count points;
Task category count points with automatic standard arguments on how well a user has done.
Awards category manually record a single points entry only, no count;
These 3 should cover everybody’s wishes.
@djpaul , it’s been a while and I’ve found a decent reason to convince you—
There are some voices require the feature of non-administration users being able to create achievements. I can see this is not only a user cap problem, but also it requires Achievements plugin accommodating events that users want to play which are beyond what the site admin want them to play. Please note, it’s different from giving cap to certain users in the administration.
For any site that gives cap to non-administration users, it needs to count the points separately.
I can vote for 3 types of Achievements that can extend the plugin’s popularity:
1. Site Achievements; —currently in play
2. Group Achievements; — feature request
3. User Achievements.—feature request
Those 3 types must be counted separately.