That's only true if the source of unreliability is stochastic.

If you have a biased study design, you'll have a systematic error; error bars will get smaller, but the results won't be more representative.

For instance, what is more likely to get a reliable measure of what people think about President Biden in the United States? (1) A survey of 100,000 people recruited solely from ads on Fox News, or (2) a random telephone survey of 3,000 people?

I'm not even certain you're grasping my objection to the 97% number. My objection is that the although the number always comes back high (> 90% in everything I've seen), it doesn't robustly come back at the same value. Why doesn't it come back at the same value? Is it because some clinics have better practices? Is it noise? Is it because of different societal pressures? Is it something else? Can we know? Do we know if the same facilitation of treatment that trans advocates call for is also liable to increase (or decrease!) regret rates?

The reason this matters is the same reason why star-ratings on Amazon matters. You don't say, "Oh, handheld vacuums overall have a rating of 4.2 stars, so handheld vacuums is good, and that's all you need to know." If some handheld vacuums have ratings of 4.7 stars and some have 3.2, the key information is the variability, not the average rating of the product as a whole, when someone tries to sell you a handheld vacuum.

If, then, someone comes up and says, "Handheld vacuums are junk. We need to ban them," the reaction should be, "This 4.7 star handheld vacuum is awesome, and we should aspire to get that one. Even if some are junk, all that means is that we shouldn't get junk." Or, in legislative terms, the counter to Ron DeSantis is "we want to emulate the Amsterdam gender identity clinic" not "97%!".

I agree that gender affirming care does tend to reduce suicide, and that the rates are really high without (and still really high with, but at least a lot better). I think the numbers you cite are a bit off the top end of what's reasonable unless either trans advocates are totally off-base on how many trans people there are, or being trans is the main reason for attempted suicide in the U.S., which would be weird given the other risk factors. Regardless, even if the number is just not-plausibly-lethal serious self-harm, it's still an issue in urgent need of attention. The attitude of most pro-trans activists completely baffles me in this regard if the problem is social disapproval. Don't you get approval by seeming agreeable and seeking compromise, which is not exactly the current state of affairs? In contrast, if the problem is lacking a strong community (even if that strong subcommunity makes the broader community uneasy), then the current state of affairs makes sense: the LGBTQ+ community more broadly and the trans- and trans-friendly community specifically do provide social approval from within. But my impression of the literature (showing that trans people who live in accepting areas have significantly lower rates of suicidal ideation) is that having a subcommunity is not enough; broad (or maybe broad-enough?) acceptance where you actually live seems to be more important.

It seems that this is an area that could benefit from greater study. For instance, does it make sense to investigate whether relocation should be a medically-approved therapy (very rare, but it is, for instance, a way to treat seasonal affective disorder, so it's not entirely unprecedented)? Obviously, concentrating trans people in smaller areas is not a good way to build society-wide acceptance, but if that's actually lifesaving for the people themselves, maybe we don't want to sacrifice them in the short run in order to achieve what seems like a reasonable long-term goal?

Anyway, this is getting pretty far afield at this point. The main issue I wanted to address was that variability is important, and that talking about averages isn't a good way to address criticisms when there is variability, because the critic will tend to assume the worst end of the spread and then some, and if you haven't tackled the issue of variability, you can't make a coherent response.

That, incidentally, goes for Covid, too. The professionals generally understand variability, but neither the left wing nor the right tends to grapple with it. For instance, although the science says that having had Covid is at least as protective as having been vaccinated, there are multiple left-wing-leaning places that say they're "following the science" by requiring full vaccination, and exclude people who...had bad reactions to the vaccine because they've had Covid and the vaccine aggravates rather than diminishes the long-lasting symptoms in their case. And despite the original vaccines having basically no efficacy against the current strains, especially after so long. So it turns out that they can't bring themselves to follow the actual science either, just the most simpleminded slogan version. (To be fair, larger organizations tend to allow medical exemptions because they hit cases like this often enough to have to do something.) Accounting for variability is important!

Indeed, the whole case for trans acceptance at all is a statement about the critical importance of accounting for variability: trans people vary from other people in important ways.