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Such a system can work...

 

as shown by the old stackfreeds which were more or less exactly what you suggest.
The main problem with the system is that you are adding friction to reduce the torque that gets to the escapement when the barrel is highly wound.  You reduce this friction as the barrel winds down.  But this friction means energy lost and reduced autonomy, reduced the power reserve.
Any of the many different constant force systems used these days is a better solution as less energy is lost to friction. thus increasing the power reserve.
There are several good articles to be found about, for example, the Lange 31 and the mechanism used for its 31 day power reserve.
Check them out.
Don

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