But how do you quantify that impact and highlight it as a strength, when a lot of it is has to do with subjunctives and hypotheticals? And how do you delicately word it on a site like LinkedIn, where the coworkers involved might happen upon it?
The truth is, when a problem is very open, there are generally far - far... far more bad candidate solutions than "good" ones. So, being able to articulately explain why an idea is bad or perhaps more likely has some mix of "good" and "bad" elements, in a manner that is irrefutable and does not diminish the courage of engineers proposing the concept in the first place, is a critical skill.
I think the key to highlighting this skill on your resume isn't stating that you know how to simply identify 'bad' solutions and say no to them, but rather that you were able to identify where solutions fell short and then led the individual or team to a solution that worked and was far superior to alternatives. After all, that's what matters. Anyone can say "no" and because of the large disparity between good and bad ideas (as described above), you'll have plenty of opportunity to do so - so, that's not very impressive. Finding the good solution [needle in the hay stack] is the skill you want to highlight... with substantive examples.
If your interested in this topic of winnowing a design space down, you may be interested in a method called Set Based Design - which is a winnowing method for mutli-objective problem sets developed by Toyota and can accelerare/automate the winnowing process.
If someone has a "bad idea" it's often not the idea that's important, its the underlying problem or motivation. The idea can be one way of having a conversation about the problem, and explore, with curiosity about lots of ideas. Then you can share the pros/cons together, and co-create a good solution.
This doesn't always work, but it helps build a relationship, instead of coming across as a jerk to the person.
This should be an internal red flag. If saying something publicly make you nervous because you know other people might have a problem with you saying it.... maybe that is not the right thing to say.
Odds are, there is a way to make such claims without it being about other people. Say nothing about talking other people into changing. Say things about the positive business impact that came to fruition because our your general advice and guidance. If you are not able to cite such positive impacts, maybe your guidance was not as strong as you think it was.
Also, I'd probably not even talk to someone who promotes themselves as talking other people out of things. Even if you were always 100% correct, it shows an ego-driven perspective which would make me worry that you aren't going to be balanced and listen when teammates need to talk you down from a bad idea.
Ultimately this is about specifics.
framing other's ideas as bad might come across as lacking humility to some.
maybe it can be framed as contributing critical ideas to design and convincing rest of the team to see why they need to revise the designs.
maybe you can mention in the passing that it is asking to talking people out of bad ideas, because they get attached to their own designs and sometimes need strong, well-articulated evidence / reasons to change their minds.