The lack of strength can come in to play with accuracy because they have to put more effort into getting the disc there. If you've got more moving parts in order to generate pop/spin/etc, there's more that can go wrong. Even on the short putts, if you're making adjustments for distance changes as small as 5-10 feet (i.e. changing your approach on a 25 footer compared to a 15 footer), you can get yourself messed up pretty easily such that any putt is a tester.
Unlike on a tee shot or a full throw, it's much more difficult to use technique (especially repeatable technique) to generate distance and accuracy with a putt. Paige Pierce can throw a drive 400 feet despite her diminutive size primarily because she has near flawless technique. There's not a whole lot of technique that can compensate for inherent lack of strength in a putting motion.
I think with Cat in particular, she's always messing around with her putting style. Sometimes subtle adjustments, sometimes significant ones. I think the more you're doing that, the more often you're going to lose the feel, occasionally out of the blue. It's hard to be consistent when you're changing things so frequently.
First, about Catrina: sometimes she putts lights out, and then sometimes... IMHO she sometimes doesn't focus enough when she's going up for short putts. And worse, sometimes she seems to get into a mental 'fog' or 'zone' where she's not giving it 100%; she gets down mentally. Sometimes she gets it back, sometimes it stays with her for the remainder of the round. She's not the only one: Paige P was becoming known for missing putts at the end of early rounds that cost her strokes, and one time cost her an outright championship instead of a co-championship when the tournament was called early due to weather. Paige P seems to have corrected that, but Catrina still has spells when she gets down.
Second, I don't disagree with most of what you've said above, but once again I'm not talking about really long putts.
For example, I'm more than twice as old as most of the MPO field and so I have no expectation of throwing 700 ft. drives or even 400 ft. drives. I'm not going to throw as far as Paul McBeth or Paige Pierce, just like I can't hit a golf ball as far as Phil Mickelson or Annika Sorenstam.
But I watch FPO golf because their strategies on holes are more like what I'd expect to have during my own rounds, just as I watched LPGA golf and volunteered at LPGA tournaments to see the same. I can't drive as far as the LPGA players nor most DG FPO players, but the iron shots into the greens and the approaches to the basket are more similar to me than trying to emulate a Mickelson wedge shot or McBeth's use of the Zone. So I believe the FPO young ladies
should be good enough to have good short games, even if they're not as physically strong as the men, and sometimes they do... just not here at the Euroopean Open, it would seem.
As a corollary to this, if an FPO player would hone her short game to dynamite status, she'd be winning all over the place. Valarie Jenkins Doss won four world titles because she could putt and approach incredibly well. When Paige P's putting is on, she's unstoppable. And part of that is to hone Course Management skills, like what Hannah Leatherman did to win the 2015 USWDGC with Paige P and Val Jenkins on the final card with her...