I haven't thought about some of the reasons to approach small publications, but the ones you point make sense.

I've tried pitching small influencers in my firm a couple of times, but we haven't had any luck so far. Maybe, their content wasn't as good in the long run, maybe they weren't motivated enough to work with us, etc. But I wouldn't be discouraged by just trying it with a few smaller influencers.

Thanks for sharing your insights on the topic!