There are a number of well known counterexamples, sports and acting unions/guilds for example.
> If you have evidence that unions don't support seniority-based promotions
I've yet to see any tech union advocate for this position, and they generally advocate against it. Tech Workers Coalition and the Alphabet Workers Union are the two I know of in this case.
> If established unions support seniority-based promotions but nascent ones don't publicly support them
This isn't really correct. Unions in certain fields support seniority based promotions. But on the other hand, certain professional fields support seniority based promotions without unions. Like medical and legal fields have non-union professional associations that afaik don't advocate for any sort of tenure based compensation. Despite that the most sought-after biglaw companies use a mostly-tenure based compensation process. The medical field uses an unholy combination of merit (exams and matching) and tenure (residency).
> This is possibly one of those issues where a union gets power and then takes overarching, unpopular measures
It's unclear how this could happen. Unions are democratic. The members vote on things. They generally cannot take unpopular measures[*]. It may be that there is a majority in some industries that prefer tenure based seniority.
[*]: Ok the exception here is if in a "Right-to-Work" state people refuse to join the union, but it still has a majority membership and is therefore NLRB recognized, so you have say, 51% employees in the union, and those 51% have a directional bias. For example, everyone who supports tenure based compensation is a union member, and they make up 26% of the company, and 52% or so of the union. Then they vote and win and the union contract includes this clause. The fix here, of course, is for other people who don't support this to join the union. But then they don't want to because of the idea that unions are bad and support unpopular policies.