On the surface, VM, what you’re saying makes sense. What makes it worse is that many seem to only go to the gedolei haposkim in order to get “yes-man” approval for what they already believe (think the famous Rav Steinman video- gaavah gaavah gaavah! Well, I guess that one didn’t work). Like you say, once someone has come out in support of one side, especially if it’s the more chumradik side, it can be futile to come out on the other.
On the other hand, people do ask their own rabbanim. If they don’t and rely on circulating kol koreis, that’s a problem. I’ve known many people who have thought that the halacha went one way and then actually asked a posek- I know that R’ Elyashiv zt”l answered my grandfather’s sheilah in a way he never expected. The mishna says aseh lecha rav, not aseh lecha pashkevil. Every situation is different and sometimes you need a real live human on the other end of the line to really answer the question.
Bottom line IMO: If what you say is really true, it shows more of a problem with the people than with the poskim. You shouldn’t be able to be convinced of a de’ah or derech via ad campaign.