Don't worry MS-P is working fine. In the style of planning you describe, you may find that status is best used to help see how up to date your plan is and use Finish Variance as you already are, to see how likely your project will deliver to the timescales promised (baseline).
The explanation you ask for is:-
MS-P is looking firstly at the status date that you have applied to your plan. Think of this as the date you are reporting up to. It then looks at the start and finish dates of all the tasks in your plan. Think of these as your forecast dates.
It then asks which of these tasks have a start date before or equal to the status date you have applied to your plan and do they have the expected % of the duration shown as complete if the task was progressed as shown in your plan.
If the % complete column has the expected % (or more)it marks the task as on 'onschedule'. Any tasks that should have started (prior to the status date) but don't have sufficient % complete will be shown as late. If the % complete field is 100%, it marks it as complete. It doesn't look at the % work complete field though only the % complete field. So it's not a good indicator of effort expenditure, but if you are only using the 'duration' field and not using the 'work' field, I wouldn't worry.
At no point is baseline being considered, just whether progress is being made as expected against your forcasted start and finish dates. Finish variance as you have noted, shows the difference between what you are forcasting and what you promised (baseline).
I still find status tracking helpful though. I use it in simple plans in conjunction with a filter to identify quickly which tasks in a plan need a progress update. If a task is showing as late in the status field, I know that either I have to apply progress (% complete) or re-plan it by extending the duration (if the work remains the same), or if no work has started, moving it forward to a date in the future when work will commence.
On the Gantt diagram, you can use 'Gridlines' to show a line for your status date that runs vertically through the entire picture. If your Gantt also shows % complete visually, you can very easily spot which parts of your plan are 'out of date'. Anything to the left of your vertical status line should either be complete of progressed upto the status line. If it isn't it needs to be replanned (unless you have a time machine and can go back and do the work on the dates in the past).
Hope this helps.