In this scenario, the product being sold is access to that following, and the influencer will - like Facebook - sell that product to anyone for any purpose. It's a bit creepy because the influencer can care not at all about the following, happily pushing crappy supplements or other junk with no qualms.
It really comes down to 'do you have any ethical or moral concerns about how your flock of followers (and perhaps a good chunk of their personal data) is being used by your paying clients'?
In contrast, consider the term 'creator' which we think of as someone producing artistic or engineering etc. value, sharing that with the world, and perhaps selling their work online, with limited (and curated) need for the junk advertising / opinion manipulation / political shenanigans cash flows.
Call people models, or actors, or by their actual professions that made them famous - they are all technically influencers but why pick such a generic term?
Otherwise IMO it’s a non-descriptive title that can be applied to pretty much anything in the public sphere.
Marque Brownlee is undeniably an influencer. Many of his videos include sponsored pitches for products like dbrand skins and he uses his rapport to give their products pseudo-reviews by showing them on his own personal phone. MKBHD is the essence of influencer, yet MKBHD fans quickly reject any such suggestion because they like MKBHD.
That is the influencer game: The closer the influencer hits to home, the less their fans see them as an influencer. We give the obvious influencer behaviors a free pass because we like the content they produce. When people don't like the content someone producers, they wave it all away as influencer content. Yet what's really happening is that the influencer is just targeting a different demographic. Same business, different audience.