I picked I don't like it

It's not like I hate every single time it happens--sometimes, it can be executed in a way that is still enjoyable.

But if you were to ask me whether I have ever encountered a version of it that I thought was better than if they had merely started at the beginning?

I would say no. I don't like cheap shock value and that's all you can really get from it.

If the best execution possible still only matches a normal "start from the beginning" execution, then that means the net effect of the gimmick itself is bad.

That's why I didn't pick "no opinion" even though the gimmick itself doesn't always make me hate the media. It still makes the media worse.

I don't like it. I don't like flashbacks in general, even more so if it's long (spanning more than one volume). this kind of thing (the topic of the poll I mean), feels way too similar to flashbacks lasting especially long, so I don't like it.

I remember clockwork planet or terror man fondly for being able to pull it off.
Others, not so much.
But those are to show there'll be character growth, and to create curiosity and tension for the rest of the whole manga/story.

So if done right, I really like it. If it's not, it can be quite annoying. I'm not a fan of flashbacks for a reason.

Some stories need to be told this way, when you want your story to start at the point where most of the narrative is taking place. If you do the "how we got here" part first, it can feel like a bait-and-switch when after the explanation you do "five years later..." Starting in the middle of the action gets the audience invested in the story right away, when starting with the background might not.

7 Seeds does this. It starts at the apocalypse, where we see the point of the seeds. We learn who the main characters are and start to root for them. If it had started with the beginning of the "7 seeds" program, and the histories of all the different groups, I think we would have lost interest before we got to the payoff.