Variance (or VEM) does change, but it's got nothing to do with averages. It's the equipment.
Each time I trade up I need to be less accurate with the ding an settings to get close, this has been highlighted in my case by a recent swap from a L20ish Cleveland wedge to a L76 Cleveland wedge of the same loft.
The new club appears completely unaffected by 40%-50% rough lies, it hits 100 yds as though it were on the fairway. The back spin is simply monstrous. I just get it roughly near the ding and roughly near the distance and it's under 2yds from the pin almost every time, even in comedy St And. wind conditions.
I'm grinding like mad now to get to L78, L80 and L83 to pick the next two Cleveland wedges and the L83 G20 set respectively.
A 59 - 60 average is very achievable once you're L83+ and have the equivalent grade equipment. Lower averages than that is then notes and practice.
I shot my first sub 60 round at Pro level, just before I made Tour Pro - not been able to repeat it since but I've been close a few times.
I'm in that horrible limbo now - tiered up to Tour Master a little too early (L74) and I'm now paying the price of not having L83+ equipment.