A generic problem with this type of reasoning is some form of the repugnant conclusion. If you don't put a Schelling fence somewhere, you end up with giving more moral weight to a large enough amount of cockroaches, bacteria or viruses than to that of humans.

In actuality, different groups of people implicitly have different Schelling points and then argue whose Schelling point is morally right. A standard Schelling point, say, 100 years ago, was all humans or some subset of humans. The situation has gotten more complicated recently, with some including only humans, humans and cute baby seals, humans and dolphins, humans and pets, or just pets without humans, etc.

So a consequentialist question would be something like

Where does it make sense to put a boundary between caring and not caring, under what circumstances and for how long?

Note this is no longer a Schelling point, since no implicit agreement of any kind is assumed. Instead, one tests possible choices against some terminal goals, leaving morality aside.