Well, you can't overhaul the freewheel's cogs in the same sense that you can overhaul the body, but some will look at the body and cogs as separate items, not wedded to each other, so which can be swapped. But of course new freewheel cogs are not commonly found sold separately!
Cog teeth that are too worn to sustain pedaling loads when a new chain is installed can often be "dressed" with a 3/8" diameter rotary stone (i.e. Dremel).
The restoration process isn't intuitive, nor is the actual mechanism by which the chain fails to hold on worn cogs!

But it can be done. By removing the rearward-facing corners of the teeth above where the wear pocket resides!
By removing just a millimeter off the point, the chain rollers of the new chain can then fall into engagement without impacting the sharp corners under hard pedaling loads, thus allowing consistent full engagement of the chain's rollers between the cog's teeth.
Thus the true cause of the slippage (failure to engage) is remedied at the source of the problem, and the freewheel can be fixed without even removing it from the bike. Usually just one or two cogs even need the slight correcting.
This doesn't refer to cogs that have become "tombstoned" by a severely-worn chain, those are just "toast", and it doesn't always work in every other case, but it has saved many freewheels for me.

The Shimano freewheels were redesigned by what I would call the best drivetrain and mass-production specialists in the industry.
What looks cheap isn't necessarily the same as what comes up short in use.
The newer Shimano freewheels are the lightest ever (outside of the expensive alloy exotics), which carries a lot of "weight" among us traditional roadie cyclists.
Their only real shortcoming is that swapping cogs is now a thing of the past with the new design. But a new one costs less than $20.