Interesting - yes - and more than a little naive. Perhaps dangerously so.
Can you imagine a mechanic telling you to rip the wires out of your car because you only need the seats to sit in? I don't imagine you'll go too far down the road.
That's the analogy I see when I read that we only need to only look after the humans - there is an explicit assumption that humans are somehow wonderfully & magically detached from this spaceship we call planet Earth - and the ecosystem services that other organisms provide w/o our intervention and most often w/o even our knowledge.
Sure the odd extinction here and there won't crash the planet - but when you look at the numbers of extinctions and the more importantly - the rate of extinctions - it is worrisome - esp. when you look at other extinction periods in history where things like the dinosaurs were wiped-out. We are a very long ways away from understanding what even a single species extinction means - let alone being able to predict what all these mass extinctions means.
https://en.wikipedia.org/wiki/Holocene_extinction
https://www.theguardian.com/environment/2015/jun/21/mass-extinction-science-warning
In addition, what do we have on this planet - almost 8 BILLION humans or so - I think we have already "looked after" the humans - maybe too well - when one looks at how sustainable that level of extraction and resource use it takes to provide for those 8 BILLION - like more resources than 1 planet has - at the level of Western Civilization needs.
https://www.livescience.com/16493-people-planet-earth-support.html