Careful. You are using reason and logic. And what you calculate from what you just said is that the stated strategy will increase volatility without increasing return. Ouch.
I liked your previous post, very good 'summary' of the goals of a trader or investor. I personally devoted the last 2 years to reducing sd only.
For fun I put the strategy above in my test-lab and indeed, var up. Had not expected this at first and had to think about it, but it probably is due expanded ranges due to streaks, both up and down. Amazing to see!