Definitely a governor issue, I can think of a couple reasons this would occur:
First, it could be that the governor is not adjusted properly. Adjustment directions can be found in this PDF Kohler service manual on page 53:
https://www.onlycubcadets.net/forum/...ead.php?t=4646
Second, it could be that the internal governor has exploded. This is somewhat common as the governors are made of plastic, and often do not age very well. In order to replace the governor, you have to completely tear apart the engine, as it's the last part you remove when disassembling the engine.
Before condemning your governor gear, try adjusting the governor and see if that helps
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'70 107 with k301 engine swap
'71 106 with 38" deck
'70 147
R with factory replacement k321, 42" deck
'61 Original with 38" timed deck
'63 70 "pinkie"
1863 with 54" deck
'46 Farmall H, '50 Farmall Cub
105 x2 (parts)