No, a new clutch spring won't cure the ill. What will cure the ill is free the variable sliding portion so it travels free the full designed distance with the belts removed. This may require removing the assembly to correct the problem. The one I repaired for a neighbor several years ago even needed new bearings. That was after I made a oak wedge to drive between the sheave sections plus some heat required to free it.
In my opinion what causes so many of these to have problems is:
1) the operator is so accustomed to using a clutch to change gears/speeds. Just don't touch the clutch after motion, both forward or revers. Only use the clutch to stop.
2) the unit remains in the ratio that's used to mow for the most of its life. Bad idea, occasionally exercise the system from speeds 1-6 or 7 while in motion, no clutch.