I am neither cherry-picking nor using yearly average figures. The one yearly figure of "over 25000 GW" is for ERCOT's installed wind capacity, which is consistent year-round apart from a small growth as new capacity comes online. My other figures are for specific dates or months, the dates being when black outs were happening.
As for why wind's low output compared to capacity matters so much, I am dealing with the inescapable facts of the Texas climate and how it relates to the energy market. The capacity in Texas is driven by summer-time demand. Yet, very rarely, there are winters in which the demand can briefly exceed summer-time capacity. It's obvious that the current market is unable to consistently meet the demand in these rare winter events.
The root problem is having capacity which can perform in summer but not in winter, whether due to not being winterized, being down for maintenance, or any other reason. Focusing solely on winterization is being used as a diversion from the problem that Texans actually care about, which is simply having power in their homes during extreme winters.
By refusing to look at the data, you are missing the fact that wind actually does produce quite a lot of power on many winter days. In fact, ERCOT's all-time record for wind production was set in February 2018. But on some winter days, wind produces very little. It should be obvious that wind significantly reduces the average profits for other generation sources in winter, and thus has a negative effect on the market for more reliable generation capacity. Wind's high variability does contribute to a lack of output during extreme weather.
The "wind performed excellently" side is just ignoring all of this, but it's all highly relevant and should be part of the discussion. I am not saying that it should lead to a "wind is bad" conclusion in the final analysis. I am saying that there are significant problems with wind generation that should be part of the analysis, not swept under the rug. Saying "just winterize" is extremely hand-wavey, as it does not account for how the high costs of winterization can result in less installed capacity, and it completely fails to consider other issues like certain generation sources being highly inconsistent even when there is no freezing. Saying "all sources had problems" is a way to avoid recognizing that nuclear dramatically outperformed every other generation source even without winterizing. Performing at 75% of capacity is completely different from performing at 12.5%.
There are some more detailed analyses in the articles at [0] and [1]. [0] deals with the claim that deregulation was the culprit, showing that the relevant Texan regulations are actually more strict and better-enforced than the national regulations (due to previous freezing issues), while other national regulations do apply to Texas (like some dealing with gas). [1] goes into detail on how capacity planning fell short, by someone who was actually responsible for capacity planning in a region of ERCOT. The main point is that Texas has no capacity market, and this is what has allowed it to become a world leader in wind generation but has led to failures in having enough capacity available. "When capacity value is rewarded, this makes the economics of renewables much less competitive. Texas has stacked the deck to make wind and solar more competitive than they could be in a system that better recognizes the value of dependable resources which can supply capacity benefits. An energy only market helps accomplish the goal of making wind and solar more competitive. Except capacity value is a real value. Ignoring that, as Texas did, comes with real perils." "Incentives and responsibility need to be paired. Doing a post-mortem on the Texas situation ignoring incentives and responsibility is inappropriate and incomplete."
[0] https://news.ycombinator.com/item?id=26186645 [1] https://news.ycombinator.com/item?id=26195050
With all this taken into account, I think that I favor a system of primarily nuclear power providing baseload needs (with some basic winterization please), and a mixture of other sources that can economically and consistently meet variable demand. This leaves wind a solid place where it is economically efficient, as in some windy regions of Texas. I haven't completely made up my mind though.