"The reason limit holdem is considered high variance for a winning player is that the win rate is relatively small."
You refer to a relationship that "is considered" to exist, but doesn't. My interpretation was that you're just saying that the variance feels bigger
because, when compared to a winrate that's smaller, it might be more times the lower winrate. As discussed in that link, this leads to more and worse downswings, but that doesn't indicate higher variance.
I'm no stats genius but I've done enough grad-level stats problems, in pencil, with only a calculator, to be very confident of how variance is calculated.
Do we agree that winrate (EV) and variance are independent?