Nick Bostrom in Infinite Ethics terms this "the causal approach" to the problem of infinities, and comments:

An advocate for the causal approach might point out that, according to relativity theory, nobody can influence events outside their future light cone. Cosmology suggests that the number of value-bearing locations (such as lives, or seconds of consciousness etc.) in our future light cone is finite. Given our best current physics, therefore, the causal approach appears to avoid paralysis.

Not so fast. Basing our ethics on an empirical fact about the laws of nature means that it cannot satisfy the highest methodological standard (cf. section 1). Well, we might be able to live with that. But the situation is much worse: the causal approach fails even in the situation we are actually in, thus failing to meet even the lowest possible acceptability criterion for a moral theory. This is because reasonable agents might— in fact, should—assign a finite non-zero probability to relativity theory and contemporary cosmology being wrong. When a finite positive probability is assigned to scenarios in which it is possible for us to exert a causal effect on an infinite number of value-bearing locations (in such a way that there is a real number r>0 such that we change the value of each of these location by at least r), then the expectation value of the causal changes that we can make is undefined.31 Paralysis will thus strike even when the domain of aggregation is restricted to our causal sphere of influence.

We could attempt to avoid this problem arising from our subjective uncertainty about the correctness of current physics by stipulating that the domain of aggregation should be restricted to our future light cone even if, contrary to special relativity, we could causally affect locations outside it. With this stipulation, we could ignore the physically far-fetched scenarios in which faster-than-light influencing is possible.

This tweak is not as good as it may appear. If, contrary to what current physics leads us to believe, it is in fact possible for us (or for somebody else, perhaps a technologically more advanced civilization) to causally influence events outside our (their) future light cone, moral considerations would still apply to such influencing. According to the present proposal, we should not factor in such considerations even if we thought superluminal propagation of causal influence to be quite likely; and that is surely wrong.

Moreover, even if the propagation of our causal effects is limited by the speed of light, it could still be possible for us to influence an infinite number of locations. This could happen, for instance, in a spatially infinite cyclic spacetime or in a steady-state cosmology.

...though this might not be relevant to Eliezer's actual reasons to reject total utilitarianism, because infinite ethics a la Bostrom would make average utilitarianism just as infeasible:

The threat is not limited to hedonistic utilitarianism. Utilitarian theories that have a broader conception of the good—happiness, preference-satisfaction, virtue, beauty-appreciation, or some objective list of ingredients that make for a good life—face the same problem. So, too, does average utilitarianism, mixed total/average utilitarianism, and prioritarian views that place a premium on the well-being of the worst off. In a canonically infinite world, average utility and most weighted utility measures are just as imperturbable by human agency as is the simple sum of utility.