This is only partially tongue-in-cheek, since the only way to reduce variance is to bet lower amounts, but this will also reduce your expected return, all the way to zero at 0$ bets.
The downside of this is that Kelly's utility function has some very nice properties. In particular the total utility of a sequence of bets will turn into a sum which means you can ignore dependencies between events. Note for instance that the argument in this article still holds even if you've got very strong dependencies between coin flips, it could repeat the pattern HTHTH forever and the Kelly criterion would still give the same optimal proportion, though obviously there are better strategies if you don't restrict yourself to blindly betting on heads.
This is a "fractional Kelly" strategy, which optimises growth under the condition that you want to reduce variance.
Also, in the real world, you never accurately know how big your % edge actually is, so there's a real chance that you are over-betting when using Kelly stakes. Using reduced stakes is a way to compensate for this.